A general framework for gravitational charges and holographic renormalization

Chandrasekaran, Venkatesa; Flanagan, Éanna É.; Shehzad, Ibrahim; Speranza, Antony J.

doi:10.1142/s0217751x22501056

A general framework for gravitational charges and holographic renormalization

Journal Article · 20 June 2022 · International Journal of Modern Physics A

DOI:https://doi.org/10.1142/s0217751x22501056· OSTI ID:1980827

Chandrasekaran, Venkatesa ^[1]; Flanagan, Éanna É. ^[2]; Shehzad, Ibrahim ^[2]; Speranza, Antony J. ^[3]

Berkeley Center for Theoretical Physics, Berkeley, CA 94720, USA; Institute for Advanced Study, Princeton, NJ 08540, USA
Department of Physics, Cornell University, Ithaca, NY 14853, USA
Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, ON, N2L 2Y5, Canada; Department of Physics, University of Illinois, Urbana-Champaign, Urbana, IL 61801, USA

We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques. This framework encompasses both localized charges associated with space–time subregions, as well as global conserved charges of the full space–time. Expressions for the charges include contributions from the boundary and corner terms in the subregion action, and are rendered unambiguous by appealing to the variational principle for the subregion, which selects a preferred form of the symplectic flux through the boundaries. The Poisson brackets of the charges on the subregion phase space are shown to reproduce the bracket of Barnich and Troessaert for open subsystems, thereby giving a novel derivation of this bracket from first principles. In the context of asymptotic boundaries, we show that the procedure of holographic renormalization can be always applied to obtain finite charges and fluxes once suitable counterterms have been found to ensure a finite action. This enables the study of larger asymptotic symmetry groups by loosening the boundary conditions imposed at infinity. We further present an algorithm for explicitly computing the counterterms that renormalize the action and symplectic potential, and, as an application of our framework, demonstrate that it reproduces known expressions for the charges of the generalized Bondi–Metzner–Sachs algebra.

Research Organization:: Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0019380; AC02-05CH11231

OSTI ID:: 1980827

Journal Information:: International Journal of Modern Physics A, Vol. 37, Issue 17; ISSN 0217-751X

Publisher:: World Scientific

Country of Publication:: United States

Language:: English

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