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GEOMETRIC ASPECTS OF THE ADS/CFT CORRESPONDENCE MICHAEL T. ANDERSON
 

Summary: GEOMETRIC ASPECTS OF THE ADS/CFT CORRESPONDENCE
MICHAEL T. ANDERSON
Abstract. We discuss classical gravitational aspects of the AdS/CFT correspondence, with the
aim of obtaining a rigorous (mathematical) understanding of the semi-classical limit of the gravita-
tional partition function. The paper surveys recent progress in the area, together with a selection
of new results and open problems.
Contents
0. Introduction 1
1. Conformally compact Einstein metrics 2
2. Uniqueness Issue. 6
3. Existence Issue. 9
4. Role of R  0. 13
5. Self-Duality. 14
6. Continuation to de Sitter and self-similar vacuum space-times. 16
References 22
0. Introduction
In this paper we discuss certain geometrical aspects of the AdS/CFT or Maldacena correspon-
dence [42], [31], [47]. From a physics point of view, only the purely classical gravitational aspects
of the correspondence on the AdS side are considered; thus no scalar, p-form or gauge elds, and
no supergravity or string corrections are considered. On the CFT side, we only take account of the

  

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics