Conformal Cauchy Slice Holography: An Alternative Phase Space For Gravity

TL;DR

This paper proposes an alternative phase space for gravity in asymptotically AdS spacetimes, replacing the Hamiltonian constraint with a Weyl-anomaly constraint, and shows how certain CFT partition functions serve as quantum gravity states.

Contribution

It introduces a new phase space framework for gravity using Weyl-anomaly constraints and connects CFT partition functions to quantum gravity states within this framework.

Findings

The alternative phase space is equivalent to the traditional one under specific conditions.

Partition functions of certain CFTs satisfy the gauge constraints in the new phase space.

This approach provides a novel perspective on quantum gravity states in AdS spacetimes.

Abstract

The phase space of gravitational theories in asymptotically Anti-de Sitter (AAdS) spacetimes consists of geometries, matter configurations, and their conjugate momenta on a Cauchy surface, subject to the Hamiltonian, momentum, and matter-gauge constraints. When a unique maximal volume slice exists in all classical solutions of the bulk equations of motion, and the matter fields satisfy certain conditions, we show that this phase space is physically equivalent to an alternative phase space in which the Hamiltonian constraint is replaced by the real Weyl-anomaly constraint, while the momentum and matter-gauge constraints remain unchanged. A necessary requirement for a functional of the metric and matter configurations to qualify as a valid quantum gravity state is that it satisfies the operator gauge constraints. Partition functions of certain conformal field theories with imaginary central charge, defined on bulk Cauchy slices, satisfy these operator gauge constraints and therefore provide candidate quantum gravity states in the alternative phase space formulation.