Preprint typeset in JHEP style - HYPER VERSIONarXiv:1110.2320 ITFA-2011-15 Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction Blaise Gout´eraux1, Jelena Smolic2, Milena Smolic2, Kostas Skenderis2,3and Marika Taylor2 1Univ Paris Diderot, Sorbonne Paris Cit´e, APC, UMR 7164 CNRS, F-75205 Paris, France 2Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam, The Netherlands 3Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1090 GL Amsterdam, The Netherlands E-mail:blaise.gouteraux@apc.univ-paris7.fr,J.Smolic@uva.nl, M.Smolic@uva.nl,K.Skenderis@uva.nl,M.Taylor@uva.nl Abstract: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. Keywords:AdS-CFT Correspondence, Gauge-gravity correspondence, Black Holes, Holography and condensed matter physics (AdS/CMT). arXiv:1110.2320v2 [hep-th] 1 Feb 2012
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