Local subsystems in gauge theory and gravity

TL;DR

This paper develops a formalism for defining localized, gauge-invariant subsystems in gauge theories and gravity by introducing boundary degrees of freedom, with implications for understanding entanglement entropy and black hole entropy.

Contribution

It introduces a boundary degrees of freedom framework for gauge theories and gravity, providing a gauge-invariant phase space and insights into entanglement and black hole entropy.

Findings

Boundary degrees of freedom are gauge choices in Yang-Mills theory.

In gravity, boundary degrees include surface location and conformal normal frame.

The formalism links entanglement entropy to boundary gluing ambiguities.

Abstract

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.