Covariant Phase Space Formalism for Fluctuating Boundaries

TL;DR

This paper extends the covariant phase space formalism to gauge theories with fluctuating boundaries, analyzing symplectic structure, charge algebra, and implications for black hole physics.

Contribution

It introduces a framework for handling boundary fluctuations in covariant phase space formalism, ensuring charge integrability and analyzing algebraic structures.

Findings

Boundary fluctuations make all surface charges integrable.

The algebra of charges and its central extensions are characterized.

Implications for black hole memory effects and semiclassical physics are discussed.

Abstract

We reconsider formulating $D$ dimensional gauge theories, with the focus on the case of gravity theories, in spacetimes with boundaries. We extend covariant phase space formalism to the cases in which boundaries are allowed to fluctuate. We analyze the symplectic form, the freedoms (ambiguities), and its conservation for this case. We show that boundary fluctuations render all the surface charges integrable. We study the algebra of charges and its central extensions, charge conservation, and fluxes. We briefly comment on memory effects and questions regarding semiclassical aspects of black holes in the fluctuating boundary setup.