Lectures on Carrollian Holography

Abstract

Carrollian Holography aims to provide a holographic description of quantum gravity in asymptotically flat spacetimes, in terms of a novel kind of `carrollian' conformal field theory defined on the spacetime null conformal boundary $\mathscr{I}$. The goal of these lectures is to offer a self-contained, pedagogical introduction to this active field of research. The main focus is given to the correspondence between massless scattering amplitudes, including gravitational amplitudes, and correlators in carrollian conformal field theory. Strong emphasis is put on the development of carrollian conformal field theory as an intrinsic, independent, and non-perturbative framework in which to formulate gravitational scattering theory.

Figures (3)

• Figure 1: Penrose diagram of Minkowski spacetime $\mathbb{M}^4$, using retarded coordinates $x^\mu=(r,u,\vec{x})$. Future null infinity $\mathscr{I}^+$ is the constant-$r$ surface in the limit $r\to \infty$. The celestial sphere $\mathbb{S}^2_u$, covered by coordinates $\vec{x}$, is a 'cut' of $\mathscr{I}^+$ at constant $u$.
• Figure 2: Illustration of the Bondi mass loss. The total mass of the system contained within the Penrose diagram and measured by an observer at $\mathscr{I}^+$ decreases in retarded time, $M_0(u_2) < M_0(u_1)$. This is because energy is radiated away in form of gravitational waves and other massless fields (red curly lines) .
• Figure 3: Application of the operator product expansion $O_1 O_2 \sim \Sigma_k O_k$ inside carrollian amplitudes. (Left) Only one OPE block contributes to the decomposition of a 3-point carrollian amplitude $\langle O_1 O_2 O_3 \rangle$, because $O_3$ projects out the all other blocks. (Right) Infinitely many OPE blocks are expected to contribute in the decomposition of 4-point carrollian amplitudes.