Holographic Dual of Linear Dilaton Black Hole in Einstein-Maxwell-Dilaton-Axion Gravity

TL;DR

This paper explores the holographic duality of rotating linear dilaton black holes, establishing a correspondence with 2D conformal field theories for both extremal and non-extremal cases, and matching their entropies via the Cardy formula.

Contribution

It demonstrates the holographic duality for rotating linear dilaton black holes, deriving the Virasoro algebra and confirming entropy matches with CFT predictions.

Findings

Virasoro algebra derived for extremal black holes

Hidden conformal symmetry identified in non-extremal case

Entropy of black holes matches CFT calculations

Abstract

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SL(2, R)$_L$$\times$SL(2, R)$_R$ Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.