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.

I will describe on -going work towards understanding holography in two -dimensional deSitter space. The hologram we  consider is an SYK-like spin model which lives on the future space-like boundary. 

The long time behaviour of a quantum chaotic system may be described using a random matrix theory, which for certain systems is dual to a 2D gravity model that allows for the creation and annihilation of baby universes.  In this talk I will present a field theory of closed topological strings, known as Kodaira-Spencer theory whose perturbative expansion reproduces the correlation functions of the matrix-theory and 2D gravity theory. To correctly describe the very long time behaviour of the correlation functions of the chaotic system  one needs to include non-perturbative effects, which in this approach are described in terms of a field theory of open topological strings, known as holomorphic Chern-Simons theory. By including a second non-perturbative saddle one reproduces the characteristic plateau behaviour of the chaotic correlators caused by the discreteness of the energy eigenvalues. 

The main purpose of this talk is to urge us to more carefully consider how random matrix models capture theories of 2D gravity. The key is to emphasize a Wignerian view alongside the more standard ’t Hooftian approach used in this area. A central observation is that without doing so, the usual narratives about the physics are incomplete. The  results prompt a proposal for a complete overhaul of how we think about  the subject, and an immediate consequence is a new proposed duality that makes holography for JT gravity (and probably other 2D gravities) much more like traditional holography in other dimensions. This provides a simple solution to the factorization puzzle, and opens up some interesting avenues of research.