I will discuss topological classification of gapped many-body Hamiltonians and their ground states in dimension d. In general, the problem is too hard as it includes diverse phenomena such as degenerate ground states on the torus, anyons, and fractons. There is, however, hope to fully understand short-range entangled, or "invertible" systems,…

We will prove a conjecture [1] on upper bound of asymptotic gap in dimension in unitary compact 2D CFT, proving it to be 1 using a "extremal" function [2]. The notion of asymptotic gap can be generalized to (h, \bar{h}) plane [3]. We will discuss how the extremal function used in [2] can be put into a bigger (natural) framework of an extremal…

The Wilsonian paradigm suggests universality of quantum field theory in the infrared. Interestingly, it also suggests universality of quantum mechanics (d=1 quantum field theory) in the ultraviolet. This suggests a study of the landscape of the infrared and the robustness of the ultraviolet. I will introduce and…

I will describe my work, all joint with D. Gaiotto and some also joint with E. Witten, to understand the homotopy type of the space of (1+1)d N=(0,1) SQFTs --- what a condensed matter theorist would call "phases" of SQFTs. Our motivating hypothesis (due in large part to Stolz and Teichner) is that this space models the spectrum called …

I will explain how the S-matrix Bootstrap for massless particles can be used to constrain the space of Effective Field Theories (EFT). In particular, I will discuss the S-matrix bootstrap for massless particles in unitary, relativistic two dimensional quantum field theories. In the context of flux tube physics, this…

The Born-Infeld model is an effective field theory of central importance describing the low-energy dynamics of massless gauge bosons on the world-volume of D-branes. Though it is in many ways an exceptional model of nonlinear electrodynamics, several aspects of the physics of the Born-Infeld model remain mysterious…

The SYK Model was originally introduced as a random matrix model for the nuclear interaction  that also describes the exponential rise of the spectral density known as  the Bethe formula. Exactly this behavior is the hallmark of the Schwarzian action, the low energy limit of the SYK model, which is the main reason for the excitement this model…

We consider supersymmetric twist and omega deformation of a type IIB brane setup involving N D3 and K D5 branes. In the large N limit, this leads to a holographic duality between two topological/holomorphic theories. We compute certain operator algebras from both sides of this topological holographic duality and…

I will discuss time-dependent probes of the renormalization group, and derive new constraints that govern the spread of local operators in holographic theories. The same methods lead to sum rules for inflationary correlators, relating observables, like the speed of sound during inflation, to properties of the UV…

We review some infinite dimensional symmetries that appear indimensionally reduced classical general relativity.  Reducing from d=4to d=2 gives a two dimensional nonlinear sigma model with an infinitedimensional affine Kac-Moody symmetry called the Geroch group.Further reducing to d=1 (along a null Kill vector)…

We review some infinite dimensional symmetries that appear indimensionally reduced classical general relativity.  Reducing from d=4to d=2 gives a two dimensional nonlinear sigma model with an infinitedimensional affine Kac-Moody symmetry called the Geroch group.Further reducing to d=1 (along a null Kill vector)…

We study the effect of ZZ instantons in c = 1 string theory, and demonstrate that they give rise to non-perturbative corrections to closed string scattering amplitudes that do not saturate unitarity within the closed string sector. Beyond the leading non-perturbative order,…

The asymptotic symmetry algebra of asymptotically flat spacetimes implies an infinity of conserved charges for 4D scattering which can be neatly recast as 2D conformal Ward identities. We cover recent progress on the proposed 4D/2D dictionary starting from the conformally soft modes that appear as currents and…

I will review some old ideas about the duality between matrix models and Liouville theory coupled to a  (p,q) minimal model. In this approach t'Hooft diagrams of the matrix model are thought of as a discretization of a 2d surface. Fine-tuning of the coupling constant leads to divergence of the perturbative expansion…

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately one scrambling…

The EHT Collaboration has recently published images of the supermassive black hole in M87. The images are dominated by a bright ring-like structure with an angular brightness asymmetry. While the diameter of this ring is resolved by the EHT, its thickness and detailed substructure are not. General relativity…

String theory on AdS3xS3xT4 with one unit of NSNS flux has been recently argued to be dual to the symmetric product orbifold of T^4. The duality has been extended to the case of generic NSNS background flux. I will consider the bosonic version of this duality and show how to match null-vector constraints on three…