Black Hole in Higher Curvature Gravity and AdS/CFT Correspondence

It is now well established that there exists the correspondence between the Supergravity theory on Anti-deSitter spacetime (AdS) and the Large N limit of Super Yang-Mills CFT. In the case of 3-d BTZ black hole , Strominger has given a simple statistical derivation of the Bekenstein-Hawking entropy via Cardy’s formula. This is an important check for the correspondence. The AdS/CFT correspondence conjectured by Maldacena is the correspondence between the Type IIB Superstring theory on AdS and the Super YangMills CFT. The string theory in general receives corrections like as Slow energy = R + α′RμνρσRμνρσ + · · · . Hence, a modest first step to the final aim is to extend AdS/CFT correspondence to higher curvature gravity. The geometrical entropy in the higher curvature gravity can be calculated by using the Noether charge method. The purpose of this paper is to give an evidence of AdS/CFT correspondence in higher curvature gravity by deriving the Iyer-Wald formula in 3-dimensions using AdS/CFT correspondence. 4