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Covariant Noether charges for type IIB and 11-dimensional supergravities

Covariant Noether charges for type IIB and 11-dimensional supergravities
Covariant Noether charges for type IIB and 11-dimensional supergravities

The covariant Noether charge formalism (also known as the covariant phase method) of Wald and collaborators, including its cohomological extension, is a manifestly covariant Hamiltonian formalism that, in principle, allows one to define and compute the energy, angular momenta, and chemical potentials of generic solutions of gravitational theories. However, it has been observed that for some supergravity solutions the variation of the Noether charge is not (at least manifestably) integrable, and as a result it is unclear whether there are well-defined thermodynamic charges for these solutions. In this work, we derive an expression for the variation of the covariant Noether charges for any solution of type IIB 10-dimensional supergravity or 11-dimensional supergravity. Although this Noether quantity is not integrable in general, we show that for asymptotically scale-invariant solutions, it is. In particular, the asymptotic scale-invariance allows one to define an energy density and conjugate chemical potentials which obey a first law of thermodynamics and a Smarr relation. These two thermodynamic relations can then be shown to imply that the variation of the Noether charge is integrable, and accordingly the energy and other thermodynamic charges may be defined unambiguously. We explicitly demonstrate and illustrate our claim by computing the thermodynamic charges of two non-trivial supergravity solutions that were recently constructed: (1) the Polchinski-Strassler black brane that is dual to the deconfined phase of N=1 theory, and (2) the CGLP black brane that asymptotes to the mass deformed Cvetič-Gibbons-Lü-Pope (CGLP) solution.

AdS/CFT, black hole thermodynamics, supergravity, symmetries and conserved charges
0264-9381
Hartnett, Gavin S
09c9c28e-7494-4793-8b1c-237b313c076a
Campos Dias, Oscar
f01a8d9b-9597-4c32-9226-53a6e5500a54
Santos, Jorge E.
6e5a1703-a14c-4ef6-bfe4-7e4c5177c274
Hartnett, Gavin S
09c9c28e-7494-4793-8b1c-237b313c076a
Campos Dias, Oscar
f01a8d9b-9597-4c32-9226-53a6e5500a54
Santos, Jorge E.
6e5a1703-a14c-4ef6-bfe4-7e4c5177c274

Hartnett, Gavin S, Campos Dias, Oscar and Santos, Jorge E. (2020) Covariant Noether charges for type IIB and 11-dimensional supergravities. Classical and Quantum Gravity, 38 (1), [015003]. (doi:10.1088/1361-6382/abc136).

Record type: Article

Abstract

The covariant Noether charge formalism (also known as the covariant phase method) of Wald and collaborators, including its cohomological extension, is a manifestly covariant Hamiltonian formalism that, in principle, allows one to define and compute the energy, angular momenta, and chemical potentials of generic solutions of gravitational theories. However, it has been observed that for some supergravity solutions the variation of the Noether charge is not (at least manifestably) integrable, and as a result it is unclear whether there are well-defined thermodynamic charges for these solutions. In this work, we derive an expression for the variation of the covariant Noether charges for any solution of type IIB 10-dimensional supergravity or 11-dimensional supergravity. Although this Noether quantity is not integrable in general, we show that for asymptotically scale-invariant solutions, it is. In particular, the asymptotic scale-invariance allows one to define an energy density and conjugate chemical potentials which obey a first law of thermodynamics and a Smarr relation. These two thermodynamic relations can then be shown to imply that the variation of the Noether charge is integrable, and accordingly the energy and other thermodynamic charges may be defined unambiguously. We explicitly demonstrate and illustrate our claim by computing the thermodynamic charges of two non-trivial supergravity solutions that were recently constructed: (1) the Polchinski-Strassler black brane that is dual to the deconfined phase of N=1 theory, and (2) the CGLP black brane that asymptotes to the mass deformed Cvetič-Gibbons-Lü-Pope (CGLP) solution.

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Covariant Noether charges - Accepted Manuscript
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Accepted/In Press date: 2 December 2019
e-pub ahead of print date: 26 November 2020
Keywords: AdS/CFT, black hole thermodynamics, supergravity, symmetries and conserved charges

Identifiers

Local EPrints ID: 445860
URI: http://eprints.soton.ac.uk/id/eprint/445860
ISSN: 0264-9381
PURE UUID: a176f3d0-5835-4b98-b0cf-22b9352fc126
ORCID for Oscar Campos Dias: ORCID iD orcid.org/0000-0003-4855-4750

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Date deposited: 12 Jan 2021 17:32
Last modified: 17 Mar 2024 06:11

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Author: Gavin S Hartnett
Author: Jorge E. Santos

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