Algebras of supersymmetry protected local and extended operators can provide analytic access to the dynamics of supersymmetric quantum field theories, even when they are strongly interacting. For example, unitary 4d N ≥ 2 superconformal field theories (SCFTs) contain a protected subsector of local operators, the so-called Schur operators, which produce an associated 2d vertex operator algebra (VOA). I will show that one can use these Schur operators to construct a fascinating web of extended operators (lines, surfaces, ...) which exist in every such SCFT. Moreover, these extended operators will mix with the local Schur operators to form a larger algebraic structure called a 2d vertex algebra. I will illustrate the richness of this mixed structure explicitly in the case of a free hypermultiplet.

In recent years, a new holographic paradigm has emerged in which simple theories of gravity in low dimensions are dual to statistical ensembles of quantum mechanical systems rather than particular quantum systems. This is a conceptual departure from the conventional holographic paradigm, particularly as realized in string theory. A hallmark of such averaged holographic dualities is the non-factorization of multi-boundary observables due to the presence of Euclidean wormholes in the bulk gravitational theory. However, more realistic holographic dualities in higher dimensions are not expected to fundamentally involve microscopic averaging. Nevertheless, there are apparently contributions to the semiclassical gravitational path integral that are associated with averaging in the boundary theory. In this talk I will attempt to reconcile these perspectives by elucidating the emergence of averaging in two different models based on recent works of mine: one top-down, the other bottom-up. In both cases, averaging of boundary degrees of freedom is an emergent phenomenon associated with the expansion around the semiclassical limit.

I will present a classification of all unitary, rational conformal field theories with two primaries, central charge c < 25, and arbitrary Wronskian index. These are shown to be either certain level-1 WZW models or cosets of meromorphic theories by such models. By leveraging the existing classification of  meromorphic CFTs of central charge c ≤ 24, all the relevant cosets are enumerated and their characters computed. This leads to 123 theories, most of which are new. It will be emphasised that this is a classification of RCFTs and not just consistent characters. Work in collaboration with Brandon Rayhaun.

This is a joint Theory/String seminar.

I describe partial progress in defining  classical and quantum entanglement entropy in string theory using the orbifold method and discuss the physical motivations from holography and black hole physics. 

Zoom:  https://uky.zoom.us/j/86707156638?pwd=VUNFUUl0cmxGMVArNXpVTTV1MGQ0QT09

In this talk, we present progress towards generalizing on-shell kinematics and color-kinematics duality to curved spacetimes. First, we define a perturbatively calculable quantity—the on-shell correlator—which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the cases of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators respectively. We then introduce a notion of on-shell kinematics for symmetric spaces in which the corresponding on-shell momenta are built from isometry generators. Using this isometric language in AdS, we compute scalar correlators and give a field-theoretic derivation of color-kinematics duality for the nonlinear sigma model. Finally, we comment on possible extensions to spacetimes without symmetry.

An inertial observer in de Sitter spacetime is always surrounded by a cosmological event horizon. This horizon shares some similarities with the black hole event horizon, which suggests the idea of using tools from holography to understand its microscopic nature. In this talk, I will describe some probes of the cosmological horizon that differ from those of black holes and comment on possible holographic interpretations of such results. 

I will discuss the thermal CFT two-point function in theories with simple holographic duals.
It encodes various aspects of the black hole geometry (orbits, quasi-normal modes, black hole singularity) in an interesting way.
I will present the exact solution to the thermal two-point function, explain its relation to the heavy-light conformal bootstrap
and discuss the connection to many-body scars. 

In this talk, we shall look at the implications of crossing symmetry, locality, and unitarity in the UV on low-energy EFT’s. We will begin by looking at 2-2 scattering amplitudes with identical external massless scalars and massive exchanges. We will introduce a crossing symmetric dispersive representation (CSDR) of the amplitude that makes full (s,t,u)-crossing symmetry manifest, unlike the usual fixed-t dispersion relations. Though the CSDR makes crossing symmetry manifest, locality is lost and has to be restored by demanding that certain spurious singularities cancel in the low energy expansion of the amplitude leading to locality constraints.

By looking at the celestial amplitude (CA) corresponding to our original 2-2 scattering amplitude we will show that the most CA’s exhibit a novel kind of positivity, which we shall argue is related to spin-0 partial wave dominance. The locality constraints imply an infinite linear system of equations that the partial wave moments of any local theory need to satisfy. By additionally imposing linear unitarity (positivity of partial wave moments), we show that these naturally lead to the phenomenon of low-spin dominance (LSD).  Finally, we show that the crossing symmetric partial waves with spurious singularities removed, dubbed as Feynman blocks have remarkable mathematical properties that can be further used to obtain two-sided bounds on low-energy Wilson coefficients.

This is based on work with Sudip Ghosh and Aninda Sinha.

In this talk, I will discuss the statistical distribution of OPE coefficients in chaotic conformal field theories. I will present the OPE Randomness Hypothesis (ORH), a generalization of ETH to CFTs which treats any OPE coefficient involving a heavy operator as a pseudo-random variable with an approximate Gaussian distribution. I will then present some evidence for this conjecture, based on the size of the non-Gaussianities and on insights from random matrix theory. Turning to the bulk, I will argue that semi-classical gravity geometrizes these statistical correlations by wormhole geometries. I will show that the non-Gaussianities of the OPE coefficients predict a new connected wormhole geometry that dominates over the genus-2 wormhole.