Edge States in Canonical Gravity

TL;DR

This paper investigates boundary (edge) states in gauge theories and gravity, motivated by black-hole entropy questions. It shows that edge observables arise in Abelian Chern-Simons theory and extend to gravity via edge-sensitive constraints and surface terms, drawing a parallel with edge dynamics in the quantum Hall effect. The quantum Hall model provides a concrete mechanism for bulk-edge coupling and perimeter-law entanglement, informing how boundary degrees of freedom might contribute to black-hole entropy. While 2+1 gravity admits an exact edge action, the 3+1 case remains open, highlighting a promising route to connect gravitational entropy with boundary information.

Abstract

It is well-known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundary. In this talk, we show how similar states arise in canonical gravity abd discuss their physical relevance using their analogy to quantum Hall effect.