Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-06-09
Class.Quant.Grav. 21 (2004) 251-264
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, RevTex file
Scientific paper
10.1088/0264-9381/21/1/017
A two-dimensional (2D) scalar-tensor gravity theory is used to describe the near-horizon near-extremal behavior of black 3-branes solutions of type IIB string theory. The asymptotic symmetry group of the 2D, asymptotically anti de Sitter (AdS) metric, is generated by a Virasoro algebra. The (non-constant) configuration of the 2D scalar field, which parametrizes the volume of the 3-brane, breaks the conformal symmetry and produces a divergent central charge in the Virasoro algebra. Using a renormalization procedure we find a finite value for the central charge and by means of the Cardy formula, the entropy of the black 3-brane in terms of microstates of the conformal field theory living on the boundary of the 2D spacetime. We find for the entropy as a function of the temperature the power-law behavior $S\propto T^3$. Unfortunately, owing to a scale symmetry of the 2D model the proportionality constant is undetermined. The black 3-brane case is a nice example of how finite temperature effects in higher dimensional AdS/CFT dualities can be described by a AdS$_2$/CFT$_1$ duality endowed with a scalar field that breaks the conformal symmetry and produces a non-vanishing central charge.
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