Constructive holography

A bstract 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 AdS d +1 spacetime. The coordinates of the collective field have a natural interpretation: the k -local collective field is a field defined on an AdS d +1 ×S k− 1 ×S ( d− 2)( k− 2) ×S d− 3 spacetime. The modes of a harmonic expansion on the S k− 1 ×S ( d− 2)( k− 2) ×S d− 3 portion of the spacetime leads to the spinning bulk fields of the dual gravity theory.