Reconstructing the spacetime dual to a free matrix

Abstract

In this paper we consider the collective field theory description of the singlet sector of a free matrix field in 2+1 dimensions. This necessarily involves the study of k-local collective fields, which are functions of 2k + 1 coordinates. We argue that these coordinates have a natural interpretation: the k-local collective field is a field defined on an AdS4×Sk−2×Sk−1 spacetime. The modes of a harmonic expansion on the Sk−2×Sk−1 portion of the spacetime leads to the spinning bulk fields of the dual gravity theory.