Publications

1. 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).
   
   

2. 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).
   
   

3. 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).
   
   

4. 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).
   
   

5. 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).
   
   

6. 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).
   
   

7. 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).
   
   

8. 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).
   
   

9. 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).
   
   

10. 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).
    
    

11. 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).
    
    

12. 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).
    
    

13. 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).
    
    

14. 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).
    
    

15. 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).
    
    

16. 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).
    
    

17. 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).
    
    

18. 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).