Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction

A bstract We show that a class of Einstein-Maxwell-Dilaton (EMD) theories are re- lated to higher dimensional AdS-Maxwell gravity via a dimensional reduction over com- pact Einstein spaces combined with continuation in the dimension of the compact space to non-integral values (‘generalized dimension...

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Bibliographic Details
Published in:The journal of high energy physics 2012-01, Vol.2012 (1), Article 89
Main Authors: Goutéraux, Blaise, Smolic, Jelena, Smolic, Milena, Skenderis, Kostas, Taylor, Marika
Format: Article
Language:English
Subjects:
Astrophysics
Chemical potential
Classical and Quantum Gravitation
Dilatons
Elementary Particles
Gravitation
High energy physics
High Energy Physics - Theory
Holography
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Reduction
Relativity Theory
Scalars
String Theory
Transport properties
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Summary:A bstract We show that a class of Einstein-Maxwell-Dilaton (EMD) theories are re- lated to higher dimensional AdS-Maxwell gravity via a dimensional reduction over com- pact Einstein spaces combined with continuation in the dimension of the compact space to non-integral values (‘generalized dimensional reduction’). This relates (fairly complicated) black hole solutions of EMD theories to simple black hole/brane solutions of AdS-Maxwell gravity and explains their properties. The generalized dimensional reduction is used to infer the holographic dictionary and the hydrodynamic behavior for this class of theories from those of AdS. As a specific example, we analyze the case of a black brane carrying a wave whose universal sector is described by gravity coupled to a Maxwell field and two neutral scalars. At thermal equilibrium and finite chemical potential the two operators dual to the bulk scalar fields acquire expectation values characterizing the breaking of con- formal and generalized conformal invariance. We compute holographically the first order transport coefficients (conductivity, shear and bulk viscosity) for this system.
ISSN:1029-8479
1126-6708
1029-8479
DOI:10.1007/JHEP01(2012)089