I will discuss recent and ongoing work with Emil Have, Stefan Prohazka and Jakob Salzer on possible kinematics for flat space holography. I will discuss how a seemingly novel projective compactification of Minkowski spacetime reveals a rich asymptotic geometry homogeneous under the Poincare group and including the blow-ups at spatial and timelike infinities as well as a novel four-dimensional space intimately associated to null infinity. This allows for novel geometric descriptions of the Minkowski asymptotic geometries and gives us a glimpse of the asymptotic geometry of asymptotically flat spaces.

Consistency with quantum gravity can impose non-trivial constraints at low energies, even if the Planck scale is at very high energy. The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. One of the most important swampland conditions is the presence of infinite towers of states becoming massless at the weak coupling/large field limits. This has been extensively tested in string theory compactifications, but a bottom-up explanation was missing. In this talk I will provide a possible explanation based on finiteness of black hole entropy. I will also explain how several wampland criteria, including the Weak Gravity Conjecture, Distance Conjecture and bounds on the finiteness of the quantum gravity vacua, may be more fundamentally a consequence of the finiteness of quantum gravity amplitudes.

The classical singularity theorems predict the existence of singularities, defined using incomplete geodesics, under a set of general assumptions. One of those assumptions, namely the energy condition, is always violated by quantum fields and thus the realm of semiclassical gravity is outside the scope of these theorems. However, quantum fields do obey weaker conditions which can also be used to predict singularities. In this talk, I will present derivations of such semiclassical singularity theorems both in the timelike and the null case and discuss the challenges and open questions for each case.

4d gauge theories with massless fermions typically have axial U(1) transformations that suffer from the ABJ anomaly. One can modify the theory of interest by adding more fields in a way that restores the axial symmetry, and use it to derive rigorous 't-Hooft anomaly matching conditions. These conditions are not valid for the original theory of interest, but for the modified theory. I will show that the modification can be done in a specific way that allows us to relate the dynamics of the modified theory to the dynamics of the original theory. In this way, the anomaly matching conditions of the modified theory can be used to learn new things on the original theory even though they involve axial transformations which are not a symmetry of the original theory. In the talk I will describe this method and discuss some applications to various examples.

Quantum mechanical theories describing large N by N matrices of oscillators can lead to an emergent space as N -> infinity. In the most fully fledged version, the emergent space is dynamical and gravitating. However, there are also simpler, lower dimensional versions of this phenomenon. One of the simplest occurs in the so-called quantum Hall matrix model, in which a 2 dimensional space emerges and supports Chern-Simons dynamics. I will describe how this solvable model leads to insights about the emergence of space from matrices. In particular, I will describe how the emergent spatial locality is reflected in the entanglement structure of the ground state of theory.

Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Recent work has determined the structure of such choices via geometric methods for various classes of non-Lagrangian theories obtained from stringy geometric engineering techniques. In this talk I will discuss a purely field theoretical counterpart of this analysis, showing that global structures can be captured from a careful analysis of the infrared Coulomb-like phases. Our results confirm and extend the many results obtained within geometric engineering about the global structures of Argyres-Douglas theories, 5d SCFTs and 6d SCFTs.

In this talk I will present some recent and ongoing work with Ashish Kakkar and Brian McPeak, where we describe a very explicit construction of a class of two-dimensional conformal field theories, denoted code CFTs. In the chiral case, code CFTs are constructed by compactifying n free bosons on a lattice, which in turn is defined from a classical error-correcting code via Construction A by Leech and Sloane. We show that constraints from higher-genus modular invariance on code CFTs can be recast into simple linear relations on the the higher-weight enumerator polynomial, which is a natural object from the code perspective. With this machinery at hand, we show that higher-genus modular invariance greatly reduces the number of seemingly consistent code CFT partition functions that were found by demanding modular invariance at genus one only. I will also cover some upcoming work, on the relation between quantum error-correcting codes and non-chiral (Narain) CFTs, and on averaging over code CFTs.

In this talk, I will review a duality between correlation function and null polygon Wilson loops and present this duality from a conformal bootstrap perspective. In the process I will also work out, in detail, a new duality between spinning three point functions in large N conformal gauge theories and null polygonal hexagonal Wilson loop.

I will introduce a class of non-invertible topological defects in (3+1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1+1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of the discrete (higher-form) symmetries. I will illustrate this by means of the example of SO(3) Yang-Mills (YM) at θ=π, as well as SU(2) N=4 SYM at τ=i.

Next-generation gravitational wave detectors require highly precise predictions for the waveforms from inspiraling black holes and neutron stars. We present advances in binary inspiral dynamics by taking classical limits of scattering amplitudes in perturbative quantum gravity. The amplitudes are calculated efficiently using modern methods for scattering amplitudes, including double copy and generalized unitarity, and loop integration techniques borrowed from collider physics. Classical physics can be extracted by several complementary approaches, including effective field theory, eikonal exponentiation, and observables in wavepacket scattering. For both conservative and dissipative dynamics of binary systems, we obtain new terms in the post-Minksowskian expansion beyond the best previous results from purely classical methods.

We will study some aspects of Quantum Chromodynamics (QCD) in d=1+1 spacetime dimensions. The theory presents many of the same challenges as d=3+1 dimensional QCD (e.g., strong interactions where perturbation theory breaks down, chiral quarks which are hard to put on the lattice, etc.). But, in 2d, there are also some special features that make the problem more tractable. We will see that one can effectively solve the system at strong coupling, revealing interesting connections to other well-studied theories such as 2d rational CFTs (minimal models, WZW models, etc.).

In this talk I will describe holographic properties of near-AdS_2 spacetimes that arise within spherically symmetric configurations of N=2 4D supergravity, for both gauged and ungauged theories. These theories pose a rich space of AdS_2xS^2 backgrounds, and their responses in the near-AdS_2 region are not universal. I will show that the spectrum of operators dual to the matter fields, and their cubic interactions, are sensitive to properties of the background and the theory it is embedded in. The properties that have the most striking effect are whether the background is BPS or non-BPS, and if the theory is gauged or ungauged. The resulting differences will have an imprint on the quantum nature of the microstates of near-extremal black holes, reflecting that not all extremal black holes respond equally when kicked away from extremality.

The strongly coupled Argyres-Douglas field theories have particular significance among four-dimensional N=2 SCFTs. In this talk, we describe new AdS5 solutions in 11d supergravity and identify them as the gravity duals of a large class of Argyres-Douglas theories, engineered via a stack of M5-branes wrapping a sphere. A notable feature of the gravity solutions is an internal M5-brane source, which is dual to an irregular puncture on the sphere. We explain how the holographic data (including central charges) match the data of the dual Argyres-Douglas field theories

Local observables in a de Sitter universe become conformal, if you wait long enough. Indeed, one can study the imprints of inflation by looking at conformal correlations in the sky. There’s an ongoing effort in the cosmology community to understand these late-time correlators from first principles, without invoking a specific Lagrangian. In this talk, I will discuss the late-time CFT living in de Sitter through the lens of a quantum field theorist. The CFT in question shares many features with its counterparts in flat space or AdS, but differs in crucial aspects: in particular, it can have complex scaling dimensions and correlation functions. I will nevertheless argue that de Sitter CFTs have good unitarity properties and can be constrained via conformal bootstrap equations. This observation should open up a new way to constrain cosmological correlation functions.

Mathematical ideas introduced by Ramanujan a century ago in number theory and combinatorics have come to play a surprising role in understanding some deep and fundamental aspects of quantum gravity and quantum field theory in three very distinct contexts of holography, duality, and topology. In this colloquium, I shall first describe the fascinating history, physics, and mathematics behind this rich and fruitful connection focusing on the role (mock) modular forms have come to play in understanding quantum properties of black holes in string theory. I shall then elucidate briefly the manifestations of mock modularity in physics in its other avatars.

It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extraordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extraordinary and special fixed points when d = 3 and N is greater or equal to 2. I'll show that formally treating N as a continuous parameter, there exists a finite range 2 < N < N_c where the extra-ordinary universality class survives, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. I'll discuss recent Monte-Carlo simulations and numerical bootstrap results that confirm the above picture and indicate that the critical value N_c > 3. Based on arXiv:2009.05119, 2111.03613, 2111.03071

We analyze black holes in deformations of Jackiw-Teitelboim (JT) supergravity by adding a gas of defects, equivalent to changing the dilaton potential. For some range of deformations, the black hole density of states extracted from the gravitational path integral becomes negative, yielding an ill-defined sum over topologies. To solve this problem, we use an equivalent matrix model description and show the negative spectrum is resolved via a phase transition analogous to the Gross-Witten transition. The matrix model contains a rich and novel phase structure that we explore in detail, using both perturbative and non-perturbative techniques.

I will describe two new quantum information theoretic probes of bulk geometry that access information inaccessible to spacelike geodesics. The first arises from considering a parallel transport process of modular Hamiltonians on the boundary under a change of state. I will show that the Berry curvature for this process computes the entanglement wedge symplectic form associated to a family of Euclidean cosmic brane solutions. Next, I will derive the circuit complexity for conformal field theory in arbitrary dimensions. I will show that circuits are dual to timelike geodesics in the bulk, and that the complexity metric admits a simple bulk geometric description in terms of distances between geodesics. In either case, these quantities are governed by the geometry of coadjoint orbits, which are special symplectic manifolds arising from group theory. The state-changing modular Berry transport process naturally describes the geometry of new, Virasoro-like coadjoint orbits that extend beyond the current classification. The complexity metric describes the geometry of a particular coadjoint orbit of the conformal group in arbitrary dimensions.

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 sum rules 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.

The Ryu-Takayanagi formula and its generalizations have led to a surprising amount of progress in our understanding of quantum gravity in the last fifteen years, culminating in the recent derivation of the Page curve in toy models of evaporating black holes. However, we still don’t understand why these formulas are true from a canonical point of view. In this talk, I will attempt to make progress on this problem by developing an analogy between gravitational entropy formulas in low-dimensional examples of holography and similar-looking formulas that have appeared in the study of entanglement entropy in emergent gauge theories. This talk will be based on 1807.06575, 2107.11872, and 2107.12634.