Our publications

1. The Hamiltonian mechanics of exotic particles
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca
   
   We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized Liouville theorem. Conserved quantities are identified via lifted Killing vectors. Extending to kinetic theory, we show that the charge current and stress tensor reproduce ideal hydrodynamics at leading order, with the ideal gas law emerging universally. Our framework provides a geometric and dynamical foundation for systems where boost invariance is absent, with applications including but not limited to: condensed matter, active matter and optimization dynamics.
   
   arXiv 2506.13848 (June 2025).
   
   

2. A note on the canonical approach to hydrodynamics and linear response theory
   Martinoia, Luca; Singh, Rajeev
   
   This note provides a comprehensive examination of the various approaches to formulating relativistic hydrodynamics, with a particular emphasis on the canonical approach. Relativistic hydrodynamics plays a crucial role in understanding the behavior of fluids in high-energy astrophysical phenomena and heavy-ion collisions. The canonical approach is explored in detail, highlighting its foundational principles, mathematical formulations, and practical implications in modeling relativistic fluid dynamics. Following this, we delve into the linear response theory, elucidating its relevance in the context of hydrodynamics. We analyze the response of relativistic fluids to external perturbations, discussing the theoretical framework and key results. This dual focus aims to bridge the gap between theoretical foundations and practical applications, offering a robust perspective on the dynamic interplay between relativistic hydrodynamics and linear response theory.
   
   Acta Phys. Pol. B 56, 1-A4 (February 2025).
   
   

3. Dissipative electrically driven fluids
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Rongen, Jonas 
   
   We consider entropy generating flows for fluids that achieve a steady state in the presence of a driving electric field. Having chosen one among the space of stationarity constraints that define such flows we show how energy and momentum relaxation are related in the presence of dissipation. Furthermore, we find that if such a fluid obeys Onsager reciprocity then the incoherent conductivity must be identically zero and consequently makes no contribution to the observable AC or DC charge conductivities.
   
   JHEP 12 114 (December 2024).
   
   

4. Thermodynamic constraints and exact scaling exponents of flocking matter
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca
   
   We use advances in the formalism of boost agnostic passive fluids to constrain transport in polar active fluids, which are subsequently described by the Toner-Tu equations. Acknowledging that the system fundamentally breaks boost symmetry, we compel what were previously entirely phenomenological parameters in the Toner-Tu model to satisfy precise relationships among themselves. Consequently, we propose a thermodynamic argument to determine the scalings of the transport coefficients under dynamical renormalization group flow given that the scaling of the noise correlator is exact, as has been supported numerically. These scalings perfectly agree with the results of recent state-of-the-art numerical simulation and experiments.
   
   Physical Review E, Volume 110, Issue 5, id.054108, 11 pp (November 2024).
   
   

5. Relaxed hydrodynamic theory of electrically driven nonequilibrium steady states
   Brattan, Daniel K.;  Matsumoto, Masataka; Baggioli, Matteo; Amoretti, Andrea
   
   The capability of hydrodynamics to accurately describe slow and long-wavelength fluctuations around nonequilibrium steady states (NESS), characterized by a stationary flow of energy or matter in the presence of a driving force, remains an open question. In this study, we explicitly construct a hydrodynamic description of electrically driven nonequilibrium charged steady states in the limit in which the relaxation of the first nonhydrodynamic excitation is parametrically slow. Our approach involves introducing gapped modes and extending the effective description into a relaxed hydrodynamic theory (RHT). Leveraging the gauge-gravity duality as a tool for controlled computations within nonequilibrium systems, we establish an ultraviolet complete model for these NESS that confirms the validity of our RHT. In summary, our findings provide a concrete realization of the validity of hydrodynamics beyond thermal equilibrium, offering valuable insights into the dynamics of nonequilibrium systems.
   
   Physical Review Research, Volume 6, Issue 4, id.043097, 14 pp (November 2024).
   
   

6. Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation
   Caselle, Michele; Magnoli, Nicodemo; Nada, Alessandro;  Panero, Marco; Panfalone, Dario; Verzichelli, Lorenzo
   
   We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.
   
   JHEP 08 198 (August 2024).
   
   

7. Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis; Rongen, Jonas
   
   We consider as a model of Weyl semimetal thermoelectric transport a (3 + 1)-dimensional charged, relativistic and relaxed fluid with a U(1)_V × U(1)_A chiral anomaly. We take into account all possible mixed energy, momentum, electric and chiral charge relaxations, and discover which are compatible with electric charge conservation, Onsager reciprocity and a finite DC conductivity. We find that all relaxations respecting these constraints necessarily render the system open and violate the second law of thermodynamics. We then demonstrate how the relaxations we have found arise from kinetic theory and a modified relaxation time approximation. Our results lead to DC conductivities that differ from those found in the literature opening the path to experimental verification.
   
   JHEP 02 071 (February 2024).
   
   

8. Restoring time-reversal covariance in relaxed hydrodynamics
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis
   
   In hydrodynamics, for generic relaxations, the stress tensor and U(1) charge current two-point functions are not time-reversal covariant. This remains true even if the Martin-Kadanoff procedure happens to yield Onsager reciprocal correlators. We consider linearized relativistic hydrodynamics on Minkowski space in the presence of energy, U(1) charge, and momentum relaxation. We then show how one can find the minimal relaxed hydrodynamic framework that does yield two-point functions consistent with time-reversal covariance. We claim the same approach naturally applies to boost agnostic hydrodynamics and its limits (e.g., Carrollian, Galilean, and Lifshitz fluids).
   
   Phys. Rev. D 108 5, 5 (September 2023).
   
   

9. Leading order magnetic field dependence of conductivities in anomalous hydrodynamics
   Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis
   
   We show that literature results claimed for the magnetic field dependence of the longitudinal conductivity in anomalous first-order hydrodynamics are frame dependent at this derivative order. In particular, we focus on (3+1)-dimensional hydrodynamics in the presence of a constant O(∂) magnetic field with a  U(1) chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. In particular, magnetic field dependent terms that were previously found in the literature only enter the nonzero frequency thermoelectric conductivities through explicitly frame dependent pieces indicating that they are not physical. This issue can be avoided entirely by incorporating the magnetic field into the fluid’s equilibrium state.
   
   Phys. Rev. D 108 1, 1 (July 2023).
   
   

10. Non-dissipative electrically driven fluids
    Amoretti, Andrea; Brattan, Daniel K.; Martinoia, Luca; Matthaiakakis, Ioannis
    
    Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid's chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. In this work, we take the first step at resolving this conundrum by introducing a new class of hydrodynamic stationary states, including an arbitrary zeroth order electric field, upon which hydrodynamics can be built. We achieve this by first writing down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives. Then we introduce suitable energy and momentum relaxation terms to balance the influence of the electric field on the fluid. This analysis leads to a new hydrostatic constraint on the spatial fluid velocity, which can be used to define our class of states. This constraint generalizes to the realm of hydrodynamics a similar constraint on the velocity found in the Drude model of electronic transport. Our class of states exhibits non-trivial thermo-electric transport even at ideal order, since it hosts non-zero DC electric and heat currents. We derive the explicit form of the corresponding conductivities and show they depend non-linearly on the electric field.
    
    JHEP 05 218 (May 2023).
    
    

11. Destroying superconductivity in thin films with an electric field
    Amoretti, Andrea; Brattan, Daniel K.; Magnoli, Nicodemo; Martinoia, Luca; Matthaiakakis, Ioannis; Solinas, Paolo
    
    In this paper, we use a Ginzburg-Landau approach to show that a suitably strong electric field can drive a phase transition from a superconductor to a normal metal. The transition is induced by taking into account corrections to the permittivity due to the superconductive gap and persists even when screening effects are considered. We test the model against recent experimental observations in which a strong electric field has been observed to control the supercurrent in superconducting thin films. We find excellent agreement with the experimental data and are able to explain several observed features. We additionally suggest a way to test our theoretical proposal via superconductor-superconductor electron tunneling.
    
    Physical Review Research, Volume 4, Issue 3, article id.033211 (September 2022).
    
    

12. Superconductors in strong electric fields: Quantum Electrodynamics meets Superconductivity
    Amoretti, Andrea
    
    A static electric field has always been thought to play little role in the physics of ideal conductors, since the screening effects of mobile carriers prevent it from penetrating deep into the bulk of a metal. Very recently however, experimental evidence has been obtained which indicates that static electric fields can be used to manipulate the superconductive properties of metallic BCS superconducting thin films, weakening the critical current. In this paper I will show how possible explanations to this striking effect can be found relying on the analogy between Superconductivity and Quantum Electrodynamics noticed by Nambu and Iona-Lasinio in the sixties. I will show that, following this parallelism, it is possible to predict a new phenomenon: the superconducting Schwinger effect. Secondly I will explain how this new microscopic effect can be connected to a modified Gizburg-Landau theory where additional couplings between electric field and the superconductive condensate are taken into account. Eventually I will connect these theoretical predictions to the experiments, proposing them as a possible explanation of the weakening of superconductivity due to an external electric field.
    
    J. Phys. Conf. Ser. 2531 1, 012001 (September 2022).
    
    

13. On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field
    Amoretti, Andrea; Brattan, Daniel K.
    
    In this paper, we review recent progress on relativistic hydrodynamics in (2 + 1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.
    
    Mod. Phys. Lett. A 37 21, 2230010 (September 2022).
    
    

14. Learning to predict target location with turbulent odor plumes
    Rigolli, Nicola; Magnoli, Nicodemo; Rosasco, Lorenzo; Seminara, Agnese
    
    Animal behavior and neural recordings show that the brain is able to measure both the intensity and the timing of odor encounters. However, whether intensity or timing of odor detections is more informative for olfactory-driven behavior is not understood. To tackle this question, we consider the problem of locating a target using the odor it releases. We ask whether the position of a target is best predicted by measures of timing vs intensity of its odor, sampled for a short period of time. To answer this question, we feed data from accurate numerical simulations of odor transport to machine learning algorithms that learn how to connect odor to target location. We find that both intensity and timing can separately predict target location even from a distance of several meters; however, their efficacy varies with the dilution of the odor in space. Thus, organisms that use olfaction from different ranges may have to switch among different modalities. This has implications on how the brain should represent odors as the target is approached. We demonstrate simple strategies to improve accuracy and robustness of the prediction by modifying odor sampling and appropriately combining distinct measures together. To test the predictions, animal behavior and odor representation should be monitored as the animal moves relative to the target, or in virtual conditions that mimic concentrated vs dilute environments.
    
    Elife (August 2022).
    
    

15. Fine corrections in the effective string describing SU (2) Yang-Mills theory in three dimensions
    Caristo, Fabrizio; Caselle, Michele; Magnoli, Nicodemo; Nada, Alessandro; Panero, Marco; Smecca, Antonio
    
    We present a study of the effective string that describes the infrared dynamics of SU(2) Yang-Mills theory in three dimensions. By combining high-precision lattice simulation results for Polyakov-loop correlators at finite temperatures close to (and less than) the deconfinement one with the analytical constraints from renormalization-group arguments, from the exact integrability of the two-dimensional Ising model that describes the universality class of the critical point of the theory, from conformal perturbation theory, and from Lorentz invariance, we derive tight quantitative bounds on the corrections to the effective string action beyond the Nambu-Gotō approximation. We show that these corrections are compatible with the predictions derived from a bootstrap analysis of the effective string theory, and have a value which does not allow to prove the Axionic String Ansatz for this model.
    
    JHEP 03 115 (March 2022).
    
    

16. Hydrodynamic magneto-transport in holographic charge density wave states
    Amoretti, Andrea; Areán, Daniel; Brattan, Daniel K.; Martinoia, Luca
    
    We employ hydrodynamics and gauge/gravity to study magneto-transport in phases of matter where translations are broken (pseudo-)spontaneously. First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field. This allows us to determine analytic expressions for all the relevant transport coefficients. Next we construct holographic models of those phases and determine all the DC conductivities in terms of the dual black hole geometry. Combining the hydrodynamic and holographic descriptions we obtain analytic expression for the AC thermo-electric correlators. These are fixed in terms of the black hole geometry and a pinning frequency we determine numerically. We find an excellent agreement between our hydrodynamic and holographic descriptions and show that the holographic models are good avatars for the study of magneto-phonons.
    
    JHEP 11 011 (November 2021).
    
    

17. On the behaviour of the interquark potential in the vicinity of the deconfinement transition
    Caristo, Fabrizio; Caselle, Michele; Magnoli, Nicodemo; Nada, Alessandro; Panero, Marco; Smecca, Antonio
    
    In the vicinity of the deconfinement transition the behaviour of the interquark potential can be precisely predicted using the Effective String Theory (EST). If the transition is continuous we can combine EST results with a conformal perturbation analysis and reach the degree of precision needed to detect the corrections beyond the Nambu-Goto approximation in the EST. We discuss in detail this issue in the case of the deconfinement transition of the SU(2) gauge theory in (2+1) dimensions (which belongs to the same universality class of the 2d Ising model) by means of an extensive set of high precision simulations. We show that the Polyakov loops correlator of the SU(2) model is precisely described by the spin-spin correlator of the 2d Ising model not only at the critical point, but also down to temperatures of the order of 0.8Tc. Thanks to the exact integrability of the Ising model we can extend the comparison in the whole range of Polyakov loop separations, even beyond the conformal perturbation regime. We use these results to quantify the first EST correction beyond Nambu-Goto and show that it is compatible with the bounds imposed by a bootstrap analysis of EST. This correction encodes important physical information and may shed light on the nature of the flux tube and of its EST description.
    
    The 38th International Symposium on Lattice Field Theory (July 2021).
    
    

18. Hydrodynamic magneto-transport in charge density wave states
    Amoretti, Andrea; Areán, Daniel; Brattan, Daniel K.; Magnoli, Nicodemo
    
    In this paper we study the dynamical properties of charged systems immersed in an external magnetic field and perturbed by a set of scalar operators breaking translations either spontaneously or pseudo-spontaneously. By combining hydrodynamic and quantum field theory arguments we provide analytic expressions for all the hydrodynamic transport coefficients relevant for the diffusive regime in terms of thermodynamic quantities and DC thermo-electric conductivities. This includes the momentum dissipation rate. We shed light on the role of the momentum dissipation rate in the transition between the pseudo-spontaneous and the purely explicit regimes in this class of systems. Finally, we clarify several relations between the hydrodynamic transport coefficients which have been observed in the holographic literature of charge density wave models.
    
    Journal of High Energy Physics, Volume 2021, Issue 05, article id. 27 (May 2021).
    
    

19. Magneto-thermal transport implies an incoherent Hall conductivity
    Amoretti, Andrea; Brattan, Daniel K.; Magnoli, Nicodemo; Scanavino, Marcello
    
    We consider magnetohydrodynamics with an external magnetic field. We find that in general one must allow for a non-zero incoherent Hall conductivity to correctly describe the DC longitudinal and Hall thermal conductivities beyond order zero in the magnetic field expansion. We apply our result to the dyonic black hole, determining the incoherent Hall conductivity in that case, and additionally prove that the existence of this transport coefficient leads to a significantly better match between the hydrodynamic and AC thermo-electric correlators.
    
    JHEP 08 097 (August 2020).
    
    

20. Energy trapped Ising model
    Amoretti, Andrea; Costagliola, Gianluca; Magnoli, Nicodemo; Scanavino, Marcello
    
    In this paper we have considered the 3D Ising model perturbed with the energy operator coupled with a nonuniform harmonic potential acting as a trap, showing that this system satisfies the trap-size scaling behavior. Eventually, we have computed the correlators ⟨𝜎⁡(𝑧)⁢𝜎⁡(0)⟩, ⟨𝜀⁡(𝑧)⁢𝜀⁡(0)⟩ and ⟨𝜎⁡(𝑧)⁢𝜀⁡(0)⟩ near the critical point by means of conformal perturbation theory. Combining this result with Monte Carlo simulations, we have been able to estimate the OPE coefficients 𝐶𝜎𝜎⁢𝜀, 𝐶𝜀𝜎⁢𝜎 and 𝐶𝜀𝜀⁢𝜀, finding a good agreement with the values obtained in [G. Costagliola, Phys. Rev. D 93, 066008 (2016), F. Kos, D. Poland, D. Simmons-Duffin, and A. Vichi, J. High Energy Phys. 08 (2016) 036].
    
    Phys. Rev. D 102, 036018 (August 2020).
    
    

21. Sauter-Schwinger effect in a Bardeen-Cooper-Schrieffer superconductor
    Amoretti, Andrea;  Solinas, Paolo;  Giazotto, Francesco
    
    Since the 1960s a deep and surprising connection has followed the development of superconductivity and quantum field theory. The Anderson-Higgs mechanism and the similarities between the Dirac and Bogoliubov–de Gennes equations are the most intriguing examples. In this last analogy, the massive Dirac particle is identified with a quasiparticle excitation and the fermion mass energy with the superconducting gap energy. Here we follow further this parallelism and show that it predicts an outstanding phenomenon: the superconducting Sauter-Schwinger effect. As in the quantum electrodynamics Schwinger effect, where an electron-positron couple is created from the vacuum by an intense electric field, we show that an electrostatic field can generate two coherent excitations from the superconducting ground-state condensate. Differently from the dissipative thermal excitation, these form a new macroscopically coherent and dissipationless state. We discuss how the superconducting state is weakened by the creation of this kind of excitations. In addition to shedding a different light and suggesting a method for the experimental verification of the Sauter-Schwinger effect, our results pave the way to the understanding and exploitation of the interaction between superconductors and electric fields.
    
    Phys. Rev. Lett. 126 11, 117001 (July 2020).
    
    

22. Hydrodynamical description for magneto-transport in the strange metal phase of Bi-2201
    Amoretti, Andrea; Meinero, Martina; Brattan, Daniel K.; Caglieris, Federico; Giannini, Enrico; Affronte, Marco; Hess, Christian; Buechner, Bernd; Magnoli, Nicodemo;  Putti, Marina
    
    High-temperature superconductors are strongly coupled systems which present a complicated phase diagram with many coexisting phases. This makes it difficult to understand the mechanism which generates their singular transport properties. Hydrodynamics, which mostly relies on the symmetries of the system without referring to any specific microscopic mechanism, constitutes a promising framework to analyze these materials. In this paper we show that, in the strange metal phase of the cuprates, a whole set of transport coefficients are described by a universal hydrodynamic framework once one accounts for the effects of quantum critical charge-density waves. We corroborate our theoretical prediction by measuring the DC transport properties of Bi-2201 close to optimal doping, proving the validity of our approach. Our argument can be used as a consistency check to understand the universality class governing the behavior of high-temperature cuprate superconductors.
    
    Phys. Rev. Research 2, 023387 (June 2020).

23. How to construct a holographic EFT for phonons
    Amoretti, Andrea
    
    These notes are based on a series of lectures given at the XV Modave Summer School in September, 2019. The course was organized in five lectures on Holographic techniques applied to condensed matter physics. In order to be self consistent, in the first three lectures I introduced the basic concepts of the so called holographic dictionary. Since AdS/CFT is by now a very well established framework to analyze strongly coupled quantum field theories, and many good reviews have been written on the topic I decided to refer to the existing literature for the basic derivation of the holographic dictionary. What illustrated in here consists instead in the analysis of a holographic model which breaks translation spontaneously or pseudo-spontaneously, the holographic realization of a charge density wave. Part of the computations outlined in this manuscript, and in particular the derivation of the Ward Identities, have never appeared in the literature so far. The paper constitute a small exercise which a reader interested in learning more advanced techniques to analyze bottom-up holographic models can use as a warm up to eventually tackle more difficult tasks.
    
    Proceedings of Science, Volume 384 - XV Modave Summer School in Mathematical Physics (April 2020).

24. Gapless and gapped holographic phonons
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in [1] continues to hold in this model for weak enough explicit breaking.
    
    JHEP 01 058 (January 2020).
    
    

25. Universal relaxation in a holographic metallic density wave phase
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    In this Letter, we uncover a universal relaxation mechanism of pinned density waves, combining gauge-gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (e.g., by disorder or lattice effects), these phonons are pinned with a mass 𝑚 and damped at a rate Ω, which we explicitly compute. This contribution to Ω is distinct from that of topological defects. We show that Ω ≃𝐺⁡𝑚2⁢Ξ, where 𝐺 is the shear modulus and Ξ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high 𝑇𝑐 superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.
    
    Phys. Rev. Lett. 123, 211602 November 2019).
    
    

26. Diffusion and universal relaxation of holographic phonons
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data of the dual background black hole solution. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent z > 2. Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solids.
    
    JHEP 10 068 (October 2019).
    
    

27. Conformal perturbation theory confronts lattice results in the vicinity of a critical point
    Caselle, Michele; Magnoli, Nicodemo; Nada, Alessandro; Panero, Marco; Scanavino, Marcello
    
    We study the accuracy and predictive power of conformal perturbation theory by a comparison with lattice results in the neighborhood of the finite-temperature deconfinement transition of SU(2) Yang-Mills theory, assuming that the infrared properties of this non-Abelian gauge theory near criticality can be described by the Ising model. The results of this comparison show that conformal perturbation theory yields quantitatively accurate predictions in a broad temperature range. We discuss the implications of these findings for the description of the critical point (belonging to the same universality class) of another strongly coupled, nonsupersymmetric non-Abelian gauge theory: the critical end point in the phase diagram of QCD at finite temperature and finite quark chemical potential.
    
    Phys. Rev. D 100, 034512 (August 2019).
    
    

28. Effective holographic theory of charge density waves
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    We use gauge/gravity duality to write down an effective low energy holographic theory of charge density waves. We consider a simple gravity model which breaks translations spontaneously in the dual field theory in a homogeneous manner, capturing the low energy dynamics of phonons coupled to conserved currents. We first focus on the leading two-derivative action, which leads to excited states with nonzero strain. We show that including subleading quartic derivative terms leads to dynamical instabilities of  translation invariant states and to stable phases breaking translations spontaneously. We compute analytically the real part of the electric conductivity. The model allows to construct Lifshitz-like hyperscaling violating quantum critical ground states breaking translations spontaneously. At these critical points, the real part of the dc conductivity can be metallic or insulating.
    
    Phys. Rev. D 97, 086017 (April 2018).
    
    

29. DC resistivity of quantum critical, charge density wave states from gauge-gravity duality
    Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele
    
    In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high  superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.
    
    Phys. Rev. Lett. 120, 171603 (April 2018).
    
    

30. Conformal perturbation theory
    Amoretti, Andrea; Magnoli, Nicodemo
    
    Statistical systems near a classical critical point have been intensively studied from both theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the experimental data of real systems. In order to compute physical quantities near a critical point, one needs to know the model at the critical (conformal) point. In this line, recent progress in the knowledge of conformal field theories, through the conformal bootstrap, gives the hope of getting some interesting results also outside of the critical point. In this paper, we will review and clarify how, starting from the knowledge of the critical correlators, one can calculate in a safe way their behavior outside the critical point. The approach illustrated requires the model to be just scale invariant at the critical point. We will clarify the method by applying it to different kind of perturbations of the 2D Ising model.
    
    Phys. Rev. D 96, 045016 (August 2017).
    
    

31. Conformal perturbation of off-critical correlators in the 3D Ising universality class
    Caselle, Michele; Costagliola, Gianluca; Magnoli, Nicodemo
    
    Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and operator product expansion coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off-critical correlators using conformal perturbation. We discuss in particular the ⟨σ(r)σ(0)⟩, ⟨ε(r)ε(0)⟩ and ⟨σ(r)ε(0)⟩ two-point functions in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the s=trΔt expansion, where t is the reduced temperature. Our results for ⟨σ(r)σ(0)⟩ agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function.
    
    Phys. Rev. D 94 2, 026005 (July 2016).
    
    

32. Chasing the cuprates with dilatonic dyons
    Amoretti, Andrea; Baggioli, Matteo; Magnoli, Nicodemo; Musso, Daniele
    
    Magnetic field and momentum dissipation are key ingredients in describing condensed matter systems. We include them in gauge/gravity and systematically explore the bottom-up panorama of holographic IR effective field theories based on bulk Einstein-Maxwell Lagrangians plus scalars. The class of solutions here examined appears insufficient to capture the phenomenology of charge transport in the cuprates. We analyze in particular the temperature scaling of the resistivity and of the Hall angle. Keeping an open attitude, we illustrate weak and strong points of the approach.
    
    JHEP 06 113 (June 2016).
    
    

33. Bounds on charge and heat diffusivities in momentum dissipating holography
    Amoretti, Andrea; Braggio, Alessandro; Magnoli, Nicodemo; Musso, Daniele
    
    Inspired by a recently conjectured universal bound for thermo-electric diffusion constants in quantum critical, strongly coupled systems and relying on holographic analytical computations, we investigate the possibility of formulating Planckian bounds in different holographic models featuring momentum dissipation. For a certain family of solutions to a simple massive gravity dilaton model at zero charge density we find linear in temperature resistivity and entropy density alongside a constant electric susceptibility. In addition we explicitly find that the sum of the thermo-electric diffusion constants is bounded.
    
    JHEP 07 102 (July 2015).
    
    

34. Analytic dc thermoelectric conductivities in holography with massive gravitons
    Amoretti, Andrea; Braggio, Alessandro; Maggiore, Nicola; Magnoli, Nicodemo; Musso, Daniele
    
    We provide an analytical derivation of the thermoelectric transport coefficients of the simplest momentum-dissipating model in gauge/gravity where the lack of momentum conservation is realized by means of explicit graviton mass in the bulk. We rely on the procedure recently described by Donos and Gauntlett for holographic models where momentum dissipation is realized through nontrivial scalars. The analytical approach confirms and supports the results found previously by means of numerical computations and the associated holographic renormalization procedure. Importantly, it also provides a precise identification of the range of validity of the hydrodynamic approximation.
    
    Phys.Rev.D 91 2, 025002 (January 2015).
    
    

35. Thermo-electric transport in gauge/gravity models with momentum dissipation
    Amoretti, Andrea; Braggio, Alessandro; Maggiore, Nicola; Magnoli, Nicodemo; Musso, Daniele
    
    We present a systematic definition and analysis of the thermo-electric linear response in gauge/gravity systems focusing especially on models with massive gravity in the bulk and therefore momentum dissipation in the dual field theory. A precise treatment of finite counter-terms proves to be essential to yield a consistent physical picture whose hydrodynamic and beyond-hydrodynamics behaviors noticeably match with field theoretical expectations. The model furnishes a possible gauge/gravity description of the crossover from the quantum-critical to the disorder-dominated Fermi-liquid behaviors, as expected in graphene.
    
    JHEP 09 160 (September 2014).
    
    

36. Holography in flat spacetime: 4D theories and electromagnetic duality on the border
    Amoretti, Andrea; Braggio, Alessandro; Caruso, Giacomo; Maggiore, Nicola; Magnoli, Nicodemo
    
    We consider a free topological model in 5D euclidean flat spacetime, built from two rank-2 tensor fields. Despite the fact that the bulk of the model does not have any particular physical interpretation, on its 4D planar edge nontrivial gauge field theories are recovered, whose features are entirely determined by the gauge and discrete symmetries of the bulk. In particular no 4D dynamics can be obtained without imposing a Time Reversal invariance in the bulk. Remarkably, one of the two possible edge models selected by the Time Reversal symmetries displays a true electromagnetic duality, which relates strong and weak coupling regimes. Moreover this same model, when considered on-shell, coincides with the Maxwell theory, which therefore can be thought of as a 4D boundary theory of a seemingly harmless 5D topological model.
    
    Phys. Rev. D 91 2, 025002 (January 2014).
    
    

37. Coexistence of two vector order parameters: a holographic model for ferromagnetic superconductivity
    Amoretti, Andrea; Braggio, Alessandro; Maggiore, Nicola; Magnoli, Nicodemo; Musso, Daniele
    
    We study a generalization of the standard holographic p-wave superconductor featuring two interacting vector order parameters. Basing our argument on the symmetry and linear response properties of the model, we propose it as a holographic effective theory describing a strongly coupled ferromagnetic superconductor. We show that the two order parameters undergo concomitant condensations as a manifestation of an intrinsically interlaced electric/magnetic dynamics. Such intertwined dynamics is confirmed by the study of the transport properties. We characterize thoroughly the equilibrium and the linear response (i.e. optical conductivity and magnetic susceptibility) of the model at hand by means of a probe approximation analysis. Some insight about the effects of backreaction in the normal phase can be gained by analogy with the s-wave unbalanced holographic superconductor.
    
    JHEP 01 054 (September 2013).
    
    

38. 3+1D Massless Weyl spinors from bosonic scalar-tensor duality
    Amoretti, Andrea; Braggio, Alessandro; Caruso, Giacomo; Maggiore, Nicola; Magnoli, Nicodemo
    
    We consider the fermionization of a bosonic-free theory characterized by the scalar-tensor duality. This duality can be interpreted as the dimensional reduction, via a planar boundary, of the topological BF theory. In this model, adopting the Sommerfield tomographic representation of quantized bosonic fields, we explicitly build a fermionic operator and its associated Klein factor such that it satisfies the correct anticommutation relations. Interestingly, we demonstrate that this operator satisfies the massless Dirac equation and that it can be identified with a Weyl spinor. Finally, as an explicit example, we write the integrated charge density in terms of the tomographic transformed bosonic degrees of freedom.
    
    Adv. High Energy Phys. 2014 635286 (August 2013).
    
    

39. Duality and Dimensional Reduction of 5D BF Theory
    Amoretti, Andrea; Blasi, Alberto; Caruso, Giacomo; Maggiore, Nicola; Magnoli, Nicodemo
    
    A planar boundary introduced \`a la Symanzik in the 5D topological BF theory, with the only requirement of locality and power counting, allows to uniquely determine a gauge invariant, non topological 4D Lagrangian. The boundary condition on the bulk fields is interpreted as a duality relation for the boundary fields, in analogy with the fermionization duality which holds in the 3D case. This suggests that the 4D degrees of freedom might be fermionic, although starting from a bosonic bulk theory. The method we propose to dimensionally reduce a Quantum Field Theory and to identify the resulting degrees of freedom can be applied to a generic spacetime dimension.
    
    Eur. Phys. J. C 73  6, 2461 (January 2013).
    
    

40. The dynamics on the three-dimensional boundary of the 4D Topological BF model
    Amoretti, Andrea; Blasi, Alberto; Maggiore, Nicola; Magnoli, Nicodemo
    
    We consider the four-dimensional (4D) abelian topological BF theory with a planar boundary, following Symanzik's method. We find the most general boundary conditions compatible with the field equations broken by the boundary. The residual gauge invariance is described by means of two Ward identities which generate a current algebra. We interpret this algebra as canonical commutation relations of fields, which we use to construct a 3D Lagrangian. As a remarkable by-product, we find a (unique) boundary condition which can be read as a duality relation between 3D dynamical variables.
    
    New J. Phys. 14 113014 (May 2012).
    
    

41. Potts correlators and the static three-quark potential
    Caselle, Michele; Delfino, Gesualdo; Grinza, P.; Jahn, Oliver; Magnoli, Nicodemo
    
    We discuss the two- and three-point correlators in the two-dimensional three-state Potts model in the high-temperature phase of the model. By using the form factor approach and perturbed conformal field theory methods we are able to describe both the large distance and the short distance behaviours of the correlators. We compare our predictions with a set of high precision Monte-Carlo simulations (performed on the triangular lattice realization of the model) finding a complete agreement in both regimes. In particular we use the two-point correlators to fix the various non-universal constants involved in the comparison (whose determination is one of the results of our analysis) and then use these constants to compare numerical results and theoretical predictions for the three-point correlator with no free parameter. Our results can be used to shed some light on the behaviour of the three-quark correlator in the confining phase of the (2+1)-dimensional SU(3) lattice gauge theory which is related by dimensional reduction to the three-spin correlator in the high-temperature phase of the three-state Potts model. The picture which emerges is that of a smooth crossover between a \Delta type law at short distances and a Y type law at large distances.
    
    J. Stat. Mech. 0603 P03008 (November 2005).
    
    

42. Exact consequences of the trace anomaly in four-dimensions
    Cappelli, Andrea; Guida, Riccardo; Magnoli, Nicodemo
    
    The general form of the stress-tensor three-point function in four dimensions is obtained by solving the Ward identities for the diffeomorphism and Weyl symmetries. Several properties of this correlator are discussed, such as the renormalization and scheme independence and the analogies with the anomalous chiral triangle. At the critical point, the coefficients a and c of the four-dimensional trace anomaly are related to two finite, scheme-independent amplitudes of the three-point function. Off-criticality, the imaginary parts of these amplitudes satisfy sum rules which express the total renormalization-group flow of a and c between pairs of critical points. Although these sum rules are similar to that satisfied by the two-dimensional central charge, the monotonicity of the flow, i.e. the four-dimensional analogue of the c-theorem, remains to be proven.
    
    Nucl. Phys. B 618 371-406 (February 2001).
    
    

43. Short distance behavior of correlators in the 2-D Ising model in a magnetic field
    Caselle, Michele; Grinza, P.; Magnoli, Nicodemo
    
    We study the spin-spin, spin-energy and energy-energy correlators in the 2d Ising model perturbed by a magnetic field. We compare the results of a set of high precision Montecarlo simulations with the predictions of two different approximations: the Form Factor approach, based on the exact S-matrix description of the model, and a short distance perturbative expansion around the conformal point. Both methods give very good results, the first one performs better for distances larger than the correlation length, while the second one is more precise for distances smaller than the correlation length. In order to improve this agreement we extend the perturbative analysis to the second order in the derivatives of the OPE constants.
    
    Nucl. Phys. B 579 635-666 (September 1999).
    
    

44. Vacuum expectation values from a variational approach
    Guida, Riccardo; Magnoli, Nicodemo
    
    In this letter we propose to use an extension of the variational approach known as Truncated Conformal Space to compute numerically the Vacuum Expectation Values of the operators of a conformal field theory perturbed by a relevant operator. As an example we estimate the VEV's of all (UV regular) primary operators of the Ising model and of some of the Tricritical Ising Model conformal field theories when perturbed by any choice of the relevant primary operators. We compare our results with some other independent predictions.
    
    Phys. Lett. B 411 127-133 (June 1997).
    
    

45. On the short distance behavior of the critical Ising model perturbed by a magnetic field
    Guida, Riccardo; Magnoli, Nicodemo
    
    We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with O.P.E. Wilson coefficients instead of correlators, all order I.R. safe formulas can be obtained for the perturbative expansion with respect to magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, that are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform have been used to compute the I.R. behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the Vacuum Expectation Value of the energy operator, left unfixed by usual nonperturbative approaches (Thermodynamic Bethe Ansatz).
    
    Nucl. Phys. B 483 563-579 (June 1996).
    
    

46. All order IR finite expansion for short distance behavior of massless theories perturbed by a relevant operator
    Guida, Riccardo; Magnoli, Nicodemo
    
    We consider here renormalizable theories without relevant couplings and present an I.R. consistent technique to study corrections to short distance behavior (Wilson O.P.E. coefficients) due to a relevant perturbation. Our method is the result of a complete reformulation of recent works on the field, and is characterized by a more orthodox treatment of U.V. divergences that allows for simpler formulae and consequently an explicit all order (regularization invariant) I.R. finitess proof. Underlying hypotheses are discussed in detail and found to be satisfied in conformal theories that constitute a natural field of application of this approach.
    
    Nucl. Phys. B 471 361-388 (November 1995).
    
    

47. Tests of QCD from jets on the Z0 peak
    Magnoli, Nicodemo; Nason, Paolo; Rattazzi, Riccardo
    
    We present a QCD analysis of some recently published data on jet production in Z 0 decays. We find that at the Z 0 energy one can analyse also jet shape variables which were disregarded at lower energy e + e − experiments because of their large hadronization sensitivity. We also discuss the possibility of extracting from the jet data certain detailed features of the colour structure of the radiative corrections to three jet production.
    
    Phys. Lett. B 252 271-281 (August 1990).
    
    

48. Duality and supersymmetry breaking in string theory
    Ferrara, Sergio; Magnoli, Nicodemo; Taylor, Tomasz; Veneziano, Gabriele
    
    Target-space duality is incorporated in previously proposed effective actions describing non-perturbative supersymmetry breaking in string theory via gaugino condensation. Duality-preserving vacua with broken supersymmetry and fixed unified coupling constant do generically occur. The question of the vanishing of the cosmological constant is also briefly addressed.
    
    Phys. Lett. B 245 409-416 (April 1990).
    
    

49. Spontaneous Breaking of Local Supersymmetry by Gravitational Instantons
    K. Konishi; Magnoli, Nicodemo; H. Panagopoulos
    
    We study the gravitino condensate 〈(D μ Ψ ν − D μ Ψ ν )(D μ Ψ ν − D ν Ψ μ )〉 in the one-loop approximation around a nontrivial background metric. It turns out that, among the known regular solutions of the euclidean Einstein equations, the Eguchi-Hanson metric is the unique relevant configuration. The standard functional integration gives a finite answer for the gravitino condensate. Due to the presence of an anomalous supersymmetry transformation law, this implies that local supersymmetry is broken spontaneously in all supergravity models with scalar multiplets.
    
    Nucl. Phys. B 309 201 (January 1988).