In recent years we have witnessed the emergence of a novel description for the physics of scattering amplitudes at the heart of which are mathematical structures called *Positive Geometries*, which loosely speaking are generalizations of polytopes having the crucial feature of encoding in their boundaries the singularity structure of…

According to Gibbons and Hawking the entropy of a dS universe is encoded in the Euclidean gravitational path integral over compact manifolds with dominant sphere saddle. In this talk I will report on recent work in which we explicitly calculate this gravitational path integral in two spacetime dimensions. Whereas the Euclidean two-dimensional…

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…

We start by revisiting the task of constructing a holographic dual to quantum gravity in asymptotically flat spacetimes. Upon recasting the S-matrix in terms of data at the conformal boundary, we see that the two standard approaches amount to slicing up the bulk and boundary in different ways.

The Celestial Hologram organizes…

Abstract:

The upper critical dimension of the O(N) vector model is well-known to be 4. In dimension 4-epsilon it is described by the Wilson-Fisher IR fixed point of the O(N) invariant scalar field theory with a small positive quartic coupling. Above 4 dimensions, this theory is non-renormalizable, but in 4+epsilon dimensions it…

I will report on my recent work with Natalie Paquette, where we derive expressions for form factors and scattering amplitudes of gauge theory as correlators of a chiral algebra. The chiral algebra is closely related to algebras appearing in the celestial holography program.

https…

Abstract: We study the *N *= 4 SYM stress tensor multiplet 4-point function for any value of the complexified coupling tau, and in principle any gauge group (we focus on SU(2) and SU(3) for simplicity). By combining non-perturbative constraints from the numerical bootstrap with two exact constraints from supersymmetric localization, we…

I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) - can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108…

Abstract: The area operator plays a central role in our understanding of holography and black hole thermodynamics. In this talk I will discuss a formulation of the area operator at the level of classical gravity, the “kink transform”, which defines a notion of a half-sided boost of gravitational initial data. I will show that it satisfies the…

**Abstract:** The past decade has seen the emergence of surprising new connections between the real-world physics of elementary particle scattering processes, and simple new mathematical structures in combinatorics, algebra and geometry. These ideas provide, in a number of examples, a different starting point for conceptualizing…

**Abstract:** Edge excitations of (2+1)D topological phases are usually described using continuum field theories. But the boundaries of some (2+1)D topological phases can also be described using lattice-like edge theories that have a finite dimensional Hilbert space for a finite size boundary. I will discuss several examples of…

This seminar will be presented **in-person in Wolfensohn Hall at the IAS and on Zoom.**

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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…

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