Constructive holography

Abstract

Abstract We consider the collective field theory description of the singlet sector of a free and massless matrix field in d dimensions. The k-local collective fields are functions of (d − 1)k + 1 coordinates. We provide a map between the collective fields and fields in the dual gravitational theory defined on AdSd+1 spacetime. The coordinates of the collective field have a natural interpretation: the k-local collective field is a field defined on an AdSd+1×Sk−1×S(d−2)(k−2)×Sd−3 spacetime. The modes of a harmonic expansion on the Sk−1×S(d−2)(k−2)×Sd−3 portion of the spacetime leads to the spinning bulk fields of the dual gravity theory.