Reconstructing the spacetime dual to a free matrix

A bstract 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 2 k + 1 coordinates. We argue that these coordinates have a natural interpretation: the k -local collective field is a field defined on an AdS 4 ×S k −2 ×S k −1 spacetime. The modes of a harmonic expansion on the S k −2 ×S k −1 portion of the spacetime leads to the spinning bulk fields of the dual gravity theory.