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Finite action in 5D gauged supergravity and the dilatonic conformal anomaly for dual quantum field theory

Finite action in 5D gauged supergravity and the dilatonic conformal anomaly for dual quantum... Gauged supergravity (SG) with a single scalar (dilaton) and arbitrary scalar potential is considered. Such dilatonic gravity describes special renormalization group flows in extended SG where scalars lie in a one-dimensional submanifold of total space. The surface counterterm and finite action for such gauged SG in three-, four-, and five-dimensional asymptotically AdS space are derived. Using a finite action and a consistent gravitational stress tensor (local surface counterterm prescription) the regularized expressions for free energy, entropy, and mass of a 4D dilatonic AdS black hole are found. The same calculation is done within standard reference background subtraction. The dilaton-dependent conformal anomaly from 3D and 5D gauged SGs is calculated using AdS conformal field theory correspondence. Such an anomaly should correspond to two- and four-dimensional dual quantum field theory which is classically and not exactly conformally invariant, respectively. The candidate c functions from 3D and 5D SGs are suggested. These c functions which have fixed points in an asymptotically AdS region are expressed in terms of a dilatonic potential and they are positively defined and monotonic for a number of potentials. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Finite action in 5D gauged supergravity and the dilatonic conformal anomaly for dual quantum field theory

Physical Review D , Volume 62 (12) – Dec 15, 2000
22 pages

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Publisher
American Physical Society (APS)
Copyright
Copyright © 2000 The American Physical Society
ISSN
1089-4918
DOI
10.1103/PhysRevD.62.124002
Publisher site
See Article on Publisher Site

Abstract

Gauged supergravity (SG) with a single scalar (dilaton) and arbitrary scalar potential is considered. Such dilatonic gravity describes special renormalization group flows in extended SG where scalars lie in a one-dimensional submanifold of total space. The surface counterterm and finite action for such gauged SG in three-, four-, and five-dimensional asymptotically AdS space are derived. Using a finite action and a consistent gravitational stress tensor (local surface counterterm prescription) the regularized expressions for free energy, entropy, and mass of a 4D dilatonic AdS black hole are found. The same calculation is done within standard reference background subtraction. The dilaton-dependent conformal anomaly from 3D and 5D gauged SGs is calculated using AdS conformal field theory correspondence. Such an anomaly should correspond to two- and four-dimensional dual quantum field theory which is classically and not exactly conformally invariant, respectively. The candidate c functions from 3D and 5D SGs are suggested. These c functions which have fixed points in an asymptotically AdS region are expressed in terms of a dilatonic potential and they are positively defined and monotonic for a number of potentials.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Dec 15, 2000

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