Holographic Renormalization in Dense Medium

Chanyong Park

doi:10.1155/2014/565219

Abstract

The holographic renormalization of a charged black brane with or without a dilaton field, whose dual field theory describes a dense medium at finite temperature, is investigated in this paper. In a dense medium, two different thermodynamic descriptions are possible due to an additional conserved charge. These two different thermodynamic ensembles are classified by the asymptotic boundary condition of the bulk gauge field. It is also shown that in the holographic renormalization regularity of all bulk fields can reproduce consistent thermodynamic quantities and that the Bekenstein-Hawking entropy is nothing but the renormalized thermal entropy of the dual field theory. Furthermore, we find that the Reissner-Nordström AdS black brane is dual to a theory with conformal matter as expected, whereas a charged black brane with a nontrivial dilaton profile is mapped to a theory with nonconformal matter although its leading asymptotic geometry still remains as AdS space.

Highlights

The Anti de Sitter (AdS)/conformal field theory (CFT) correspondence [1,2,3,4,5] is a fascinating tool in studying the strongly interacting system like quantum chromodynamics (QCD) or condensed matter system
In the extremal limit of a Reissner-Nordstrom AdS (RNAdS) black brane we find that the Fermi surface energy of the dual field theory is proportional to N1/3 in the UV limit, where N denotes the number of quark
We have studied the holographic renormalization of the charged black branes whose asymptotic geometry is given by an AdS space

Summary

Introduction

The AdS/CFT correspondence [1,2,3,4,5] is a fascinating tool in studying the strongly interacting system like quantum chromodynamics (QCD) or condensed matter system. In [12, 13], it was shown that adding local counter terms to the AdS boundary makes the on-shell gravity action finite and that quantities derived from it can be reinterpreted as those of the dual CFT This holographic renormalization has been generalized even to the non-AdS geometries like the Lifshitz geometry [23,24,25,26,27,28] and Einstein-dilaton gravity [29,30,31,32,33,34,35,36,37,38,39]. Since there is no asymptotic freedom in the holographic dual CFT, one can not directly interpret it as free relativistic fermions We consider another charged black brane in the EinsteinMaxwell-dilaton theory in which the holographic renormalization leads to the consistent physical quantities satisfying the thermodynamic law.

Holographic Renormalization of the RNAdS Black Brane

Holographic Nonconformal Matter in the Asymptotic AdS Geometry

Discussion