Asymptotic Symmetries in the Gauge Fixing Approach and the BMS Group

TL;DR

This paper introduces asymptotic symmetries in gauge theories, focusing on general relativity, boundary conditions, and charges, with applications to BMS group extensions, holography, and black hole physics.

Contribution

It provides a comprehensive overview of deriving asymptotic symmetries and charges in gauge theories, emphasizing the BMS group and its extensions in various spacetime asymptotics.

Findings

Extended BMS groups relevant for holography

Connections between asymptotic symmetries and soft theorems

Implications for black hole information paradox

Abstract

These notes are an introduction to asymptotic symmetries in gauge theories, with a focus on general relativity in four dimensions. We explain how to impose consistent sets of boundary conditions in the gauge fixing approach and how to derive the asymptotic symmetry parameters. The different procedures to obtain the associated charges are presented. As an illustration of these general concepts, the examples of four-dimensional general relativity in asymptotically (locally) (A)dS$_4$ and asymptotically flat spacetimes are covered. This enables us to discuss the different extensions of the Bondi-Metzner-Sachs-van der Burg (BMS) group and their relevance for holography, soft gravitons theorems, memory effects, and black hole information paradox. These notes are based on lectures given at the XV Modave Summer School in Mathematical Physics.