Asymptotic symmetries and geometry on the boundary in the first order formalism

TL;DR

This paper explores how the first order formalism provides a clearer understanding of boundary geometry and asymptotic symmetries across various spacetime backgrounds, advancing holography beyond AdS spaces.

Contribution

It demonstrates that the first order formalism naturally encodes asymptotic symmetries as gauged algebras, simplifying analysis and offering new insights into boundary structures in diverse spacetimes.

Findings

Asymptotic symmetry algebra is realized as a gauged symmetry in first order variables.

First order formalism geometrizes boundary analysis, simplifying the study of asymptotic structures.

New perspective on scale versus conformal invariance in AdS/CFT correspondence.

Abstract

Proper understanding of the geometry on the boundary of a spacetime is a critical step on the way to extending holography to spaces with non-AdS asymptotics. In general the boundary cannot be described in terms of the Riemannian geometry and the first order formalism is more appropriate as we show. We analyze the asymptotic symmetries in the first order formalism for large classes of theories on AdS, Lifshitz or flat space. In all cases the asymptotic symmetry algebra is realized on the first order variables as a gauged symmetry algebra. First order formalism geometrizes and simplifies the analysis. We apply our framework to the issue of scale versus conformal invariance in AdS/CFT and obtain new perspective on the structure of asymptotic expansions for AdS and flat spaces.