Seminars

Abstract: It has long been speculated that a black hole in string theory turns into highly excited strings close to the Hagedorn temperature. Gravitational attraction pulls different parts of the string together, forming a star-like configuration. In this talk, I will review the properties of a concrete solution of this kind, first discovered by Horowitz and Polchinski. I will discuss whether the Horowitz-Polchinski solution can be smoothly connected with the black hole as worldsheet CFTs. If time permits, I will discuss an ongoing work on the spectral form factor of a gas of strings, which probes the finer details of the spectrum. I will highlight the importance of a potential family of generalizations of the Horowitz-Polchinski solution.

Abstract: In this talk I will discuss two aspects of continuum field theories of fractons. These models have been of recent interest to condensed matter and high energy theorists. On the one hand they are candidates for new phases of quantum matter, and on the other, they have features which seem impossible to describe in continuum field theory, including quasiparticles of restricted mobility and a ground state degeneracy which depends sensitively on the ultraviolet.

The two aspects I will discuss are (i.) some soluble interacting large N versions of these models, and (ii.) the coupling of these models to a spacetime background, useful for obtaining Ward identities for response functions. Our large N results show in detail the importance of interactions, and how a careful treatment of the path integral in continuum field theory can reproduce the exotic features mentioned above.

Abstract: I consider a free Maxwell field in four dimensions in the presence of a codimension two defect. Reflection positive, codimension two defects which preserve conformal symmetry in this context are very limited. Only generalized free fields can exist on the defect and interact with the free Maxwell field in the bulk. This result stands in stark contrast to the boundary case where interacting conformal boundary conditions can be found for free bulk fields, producing systems with physical relevance, for example for graphene.

Abstract: We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iε prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to "skeleton" diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with "diagonal", box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles.

Abstract: Crossing symmetry is responsible for a number of CFT constraints, including the famed Cardy density of states. In this talk I will review how crossing symmetry of four- and higher-point functions can be used to extract the density of products of OPE coefficients, deriving new universal formulas along the way. These formulas are theory independent, and therefore can be used e.g. to prove refined bounds using the conformal bootstrap. We will end with some comments on the dual interpretation of these results.

Abstract: Recent years have seen remarkable progress in our understanding of black holes and the information paradox: for black holes in AdS coupled to a bath, Page curves consistent with unitarity have been obtained through semi-classical computations involving quantum extremal surfaces. These discussions have largely been based on two-dimensional models where gravity is solvable and on bottom-up models which may or may not make sense as consistent theories of quantum gravity. In this talk we will discuss simple top-down models for black hole information transfer based on twisted compactifications of concrete CFTs in various dimensions and their holographic duals.

Abstract: I will present a bulk reconstruction technique in AdS/CFT suitable for addressing a facet of the black hole information problem: how to unambiguously predict the results of measurements accessible to an infalling observer in the black hole interior. I will explicitly apply the method in the AdS_2/SYK correspondence and comment on its generalizations.

Abstract: Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EoS) at densities and temperatures realised inside neutron stars and their mergers is a long-standing open problem. I will present a framework for the EoS of dense and hot QCD that describes the deconfinement phase transition between a dense baryonic and quark matter phase via the holographic V-QCD model. I will show some predictions of this model for the properties of isolated and binary neutron star systems and discuss the formation of quark matter in their post-merger stage.

Abstract: In this talk we will discuss a class of AdS5 solutions of type IIB supergravity that are dual to marginal deformations of N = 1 conformal field theory. Using generalised geometry, we show how the geometry encodes the information about the holomorphic data of the dual SCFT and how this allows to count protected operators, Hilbert series etc. This construction generalises what is done for N=1 SCFT dual to Sasaki-Einstein manifolds. We apply the construction to the long-standing problem of finding the gravity dual of the generic N = 1 deformations of N = 4 conformal field theory. While we are not able to find the explicit supergravity backgrounds, continuity argument allow to proof its existence.

Abstract: In this talk I will discuss aspects of microscopic degrees of freedom of gravity as motivated by string theory. Although these are expected to be generically quantum mechanical, our goal is to understand a class of such states that are coherent enough to admit classical descriptions in Einstein gravity. The construction of such states corresponds to adding interesting topological structures in spacetime with the help of compact extra dimensions. The constructions manifestly behave like ultra compact objects, dubbed topological stars, which can also model black hole microstates. I will also discuss the classical and quantum mechanical stability of the spherically symmetric class.

Abstract: I will present a bulk reconstruction technique in AdS/CFT suitable for addressing a facet of the black hole information problem: how to unambiguously predict the results of measurements accessible to an infalling observer in the black hole interior. I will explicitly apply the method in the AdS_2/SYK correspondence and comment on its generalizations.

Abstract: In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. We provide explicit constructions in the boundary theory of infalling time evolutions which can take bulk observers behind the horizon. The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III1 von Neumann algebraic structure and the half-sided modular translation structure associated with it.

Abstract: I discuss theories of fractons, with a focus on the role of foliated field theories and field theories with exotic symmetry in their construction. I then turn to the realization — on systems of branes in string theory — of several novel theories of this sort.

Abstract: String/M-theory compactifications may suffer from instabilities, which are generically difficult to analyze. I will consider this issue from a higher dimensional perspective. I will first focus on supersymmetric vacua, showing how to adapt familiar positive-energy theorems directly to M-theory and type II supergravity, rather than to their effective lower-dimensional reductions, and showing how to consistently include localized sources. I will then discuss how one might extend these results to non-supersymmetric vacua.

Abstract: There are several important conceptual and computational questions concerning path integrals which have recently been approached from new perspectives motivated by "resurgent asymptotics", a novel mathematical formalism that seeks to unify perturbative and non-perturbative physics. This talk will review the basic ideas behind the connections between resurgent asymptotics and physics, starting from the work of Airy and Stokes, and the development of trans-series by Ecalle, and then turn to several recent applications in quantum mechanics and quantum field theory. The main motivation is to develop a deeper understanding of field theoretic path integrals directly from a saddle point Lefschetz thimble decomposition, and also by reconstruction from perturbative information.

Abstract: In this talk, I will discuss patterns of entanglement and information flow between the hard and soft particles produced in QED scattering procesees. Specifically, I will discuss the scaling of the Renyi and the entanglement entropies with the IR cutoff, at fixed order in perturbation theory, as well as to all orders, in the large volume limit. The leading perturbatve entanglement entropy is logarithmically divergent, with the coefficient exhibiting universality properties. In a particular kinematical limit, it is proportional to the cusp anomalous dimension of QED. The all orders Renyi entropies are free of IR divergences. On the other hand, the entanglement entropy retains non-analytic behavior with respect to the IR cutoff even to all orders in perturbation theory.

Abstract: In the context of fracton physics, an interesting class of field theories has emerged that enjoys dipole symmetry. In this talk I will discuss complex scalar theories with dipole symmetry and present a nogo-theorem that states that such a theory cannot simultaneously be Gaussian, have linearly realised dipole symmetry and contain gradient terms. Another way of putting this is that a Gaussian theory with linear dipole symmetry must be Carrollian. I will then discuss the Noether procedure that leads to the gauging of dipole symmetry and discuss the resulting gauge theory from a Hamiltonian perspective. The resulting gauge theory is a gauge theory for a scalar and a symmetric tensor gauge field. It has a rich spectrum of propagating modes, and I will discuss its coupling to worldline actions. Finally, I will turn to the topic of how to couple these scalar and gauge theories to curved spacetime. It turns out that the relevant geometry is known as Aristotelian geometry, a geometric structure that has also appeared elsewhere in the literature, whenever the theory has no boost symmetry.

Abstract: I will introduce a novel numerical approach for solving the conformal-bootstrap equations with Reinforcement Learning. I will apply this to the case of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compactified scalar, but the method can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.

Abstract: Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension ∆ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on R × S3^{3}3.

Abstract: U(N) supersymmetric Yang-Mills theory naturally appears as the low-energy effective theory of a system of N D-branes and open strings between them. Transverse spatial directions emerge from scalar fields, which are N x N matrices with color indices; roughly speaking, the eigenvalues are the locations of D-branes. In the past, it was argued that this simple 'emergent space' picture cannot be used in the context of gauge/gravity duality, because the ground-state wave function delocalizes at large N, leading to a conflict with the locality in the bulk geometry. In this paper we show that this conventional wisdom is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. This conclusion is obtained by clarifying the meaning of the 'diagonalization of a matrix' in Yang-Mills theory, which is not as obvious as one might think. This observation opens up the prospect of characterizing the bulk geometry via the color degrees of freedom in Yang-Mills theory, all the way down to the center of the bulk.

Abstract: It has been a long-standing conjecture that any CFT with a large central charge and a large gap M in the spectrum of single-trace operators must be dual to a local effective field theory in AdS. In my talk, I will discuss a proof of a sharp form of this conjecture. In particular, I will explain how to derive numerical bounds on bulk Wilson coefficients in terms of M using the conformal bootstrap. The bounds exhibit scaling in M expected from dimensional analysis in the bulk. The main technical tools are dispersive CFT sum rules. These provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows one to apply recently-developed flat-space methods to construct positive CFT functionals. My talk will be based on https://arxiv.org/pdf/2106.10274.pdf, which is joint work with S. Caron-Huot, L. Rastelli, and D. Simmons-Duffin.

Abstract: Our fundamental description of the Universe is filled with hierarchies and it is an important theoretical question to understand their origin. An elegant mechanism to generate large hierarchies is that of Fixed Point Annihilation (FPA), in which a pair of fixed points of the Renormalization Group merge and migrate to the complex plane. This is believed to be responsible for the walking behavior of some gauge theories or the appearance of weak first-order transitions in condensed-matter models. In this talk we will discuss the physics of these complex fixed points, the possibility of defining complex Conformal Field Theories (CFTs) associated to them and how the presence of several complex conjugate pairs can have a substantial impact on the generated hierarchies. We will present weakly coupled field-theory examples and propose a gravitational dual to FPA, the resulting complex fixed points and their related complex CFTs at strong coupling.

Abstract: I will show how one can solve numerically for the energy levels of certain quantum mechanical systems using a recursive plus unitarity method.  This method, called "bootstrap", uses the equations of motion of the system to find recursions between certain expectation values in an energy eigenstate.  Combined with positivity of the expectation value of any positive operator (what one calls unitarity), one finds relations to classic problems in mathematics: the moment problem.  One can check this positivity numerically and theorems guarantee the existence of a probability measure that solves the moment problem if certain conditions are satisfied.

Abstract: We study the real time formation of the ground state of two coupled SYK models. This is a highly entangled state which is close to the thermofield double state and can be viewed as a wormhole. We start from a high temperature state, we let it cool by coupling it to a cold bath. We numerically solve for the large N dynamics. Our main result is that the system forms a wormhole by going through a region with negative specific heat, taking time that is independent of N. The dynamics is smooth everywhere and it seems to follow the equilibrium thermodynamic configurations of the microcanonical ensemble. Also we comment on the relation between this coupled SYK model and Jackiw-Teitelboim gravity theory with bulk fields.

Abstract: We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and two-dimensional holographic conformal field theories. This is a refined, "microcanonical" version of K-complexity that applies to theories with infinite or continuous spectra (including quantum field theories), and in the holographic theories we study exhibits exponential growth for a scrambling time, followed by linear growth until saturation at a time exponential in the entropy —a behavior that is characteristic of chaos. We show that the linear growth regime implies a universal random matrix description of the operator dynamics after scrambling. Our main tool for establishing this connection is a "complexity renormalization group" framework we develop that allows us to study the effective operator dynamics for different timescales by "integrating out" large K-complexities. In the dual gravity setting, we comment on the empirical match between our version of K-complexity and the maximal volume proposal, and speculate on a connection between the universal random matrix theory dynamics of operator growth after scrambling and the spatial translation symmetry of smooth black hole interiors.

Abstract: Bulk reconstruction in the AdS/CFT correspondence is a key idea revealing the mechanism of it, and various methods were proposed to solve the inverse problem. We use deep learning and identify the neural network as the emergent geometry, to reconstruct the bulk. The lattice QCD data such as chiral condensate, hadron spectra or Wilson loop is used as input data to reconstruct the emergent geometry of the bulk. The requirement that the bulk geometry is a consistent solution of an Einstein-dilaton system determines the bulk dilaton potential backwards, to complete the reconstruction program. We demonstrate the determination of the bulk system from QCD lattice/experiment data.

Abstract: Carroll symmetry arises from Poincare symmetry upon taking the limit of vanishing speed of light. I will start with a pedagogical introduction to Carroll symmetry, Carroll particles and Carroll field theories. Then I will discuss some applications of Carroll symmetry at the level of fluids and cosmology, showing in particular that Carroll symmetry might be relevant for dark energy and inflation. Finally, I will comment on Carroll gravity by considering the small speed of light expansion of general relativity.

Abstract: I will discuss the fundamentals of quantum field theory on a rigid de Sitter space. First, I will show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. This finding systematizes recent findings in the literature on the relation between dS and AdS Feynman diagrams, as well as allows us to establish basic properties of these correlators, which comprise a Euclidean CFT. Second, I use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Third, I will prove that unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. This statement does not rely on the use of Euclidean AdS Lagrangians and holds non-perturbatively.

Abstract: After reviewing the role Quasi-Normal Modes (QNMs) play in the Gravitational Wave (GW) signals emitted in the ring-down phase of Black-Hole (BH) mergers, we present a novel efficient approach to compute QNMs of BHs, D-branes and fuzz-balls, based on quantum Seiberg-Witten (SW) curves for N=2 supersymmetric Yang-Mills (SYM) theories. We find remarkable agreement with numerical results obtained by means of Leaver's method of continuous fractions and with `semi-classical' results obtained in the eikonal approximation, based on geodetic motion. Finally we discuss the extension to D3-branes and their bound states of Couch-Torrence (CT) conformal inversions, that exchange horizon and infinity, and show that they keep the photon-sphere (or photon-halo) fixed.

Abstract: Recently discovered solvable lattice models, known as fractons, have forced us to rethink the very basic question of what a quantum field theory is. In order to describe the continuum limit of fracton lattice models, novel quantum field theories had to be written down that go beyond what textbooks taught us, exhibiting unusual features such as subsystem symmetries, UV sensitivity of IR quantities, and broken rotation invariance. This talk will describe several explorations of the interesting new properties these unusual field theories exhibit.

Abstract: We study Quantum Field Theory (QFT) on a background de Sitter spacetime dS_d+1. Our main tool is the Hilbert space decomposition in irreducible unitarity representations of its isometry group SO(d+1,1). Throughout this work, we focus on the late-time physics of dS_d+1, in particular on the boundary operators that appear in the late-time expansion of bulk local operators. As a first application of the Hilbert space formalism, we recover the Källen-Lehmann spectral decomposition of bulk two-point functions. In the process, we exhibit a relation between poles in the corresponding spectral densities and boundary CFT data. Next, we study the conformal partial wave decomposition of four-point functions of boundary operators. These correlation functions are very similar to the ones of standard conformal field theory, but have different positivity properties that follow from unitarity in de Sitter. We conclude by proposing a non-perturbative conformal bootstrap approach to the study of these late-time four-point functions, and we illustrate our proposal with a concrete example for QFT in dS_2.

Abstract: Finding phenomenological vacua that are on a trustworthy footing within string theory is hard. Some crucial properties of such vacua are: moduli stabilisation and a small cosmological constant in units of the fundamental scale. In this talk I will review the progress on achieving this for SUSY AdS vacua.