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

DOI10.1088/0264-9381/21/1/017zbMATH Open1061.83055arXivhep-th/0306069OpenAlexW3102744845MaRDI QIDQ4467259

Mariano Cadoni

Publication date: 9 June 2004

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Abstract: 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 $Spropto{T}^3$. 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.

Full work available at URL: https://arxiv.org/abs/hep-th/0306069

zbMATH Keywords

Virasoro algebraconformal symmetry

Mathematics Subject Classification ID

String and superstring theories in gravitational theory (83E30) Analogues of general relativity in lower dimensions (83C80)

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