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A two-dimensional (2D) scalar-tensor gravity theory is used to describe thenear-horizon near-extremal behavior of black 3-branes solutions of type IIBstring theory. The asymptotic symmetry group of the 2D, asymptotically anti deSitter (AdS) metric, is generated by a Virasoro algebra. The (non-constant)configuration of the 2D scalar field, which parametrizes the volume of the3-brane, breaks the conformal symmetry and produces a divergent central chargein the Virasoro algebra. Using a renormalization procedure we find a finitevalue for the central charge and by means of the Cardy formula, the entropy ofthe black 3-brane in terms of microstates of the conformal field theory livingon the boundary of the 2D spacetime. We find for the entropy as a function ofthe temperature the power-law behavior $S\propto T^3$. Unfortunately, owing toa 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 inhigher dimensional AdS/CFT dualities can be described by a AdS$_2$/CFT$_1$duality endowed with a scalar field that breaks the conformal symmetry andproduces a non-vanishing central charge.Comment: 10 pages, RevTex fil

Entropy of the 3-brane and the AdS/CFT duality from a two-dimensional perspective