Gravitational dynamics from collective field theory

TL;DR

This paper explores how collective field theory provides a systematic way to understand the holographic duality in AdS/CFT, highlighting the redundancy of degrees of freedom that enables a gravitational description from a non-gravitational theory.

Contribution

It proposes that the over completeness of collective fields explains the emergence of holography and demonstrates how bulk degrees of freedom relate to boundary data.

Findings

Collective field theory's redundancy underpins holographic duality.

Bulk degrees of freedom can be reconstructed from boundary neighborhoods.

Evidence supports collective fields as a mechanism for gravity emergence.

Abstract

We consider the relevance of a collective field theory description for the AdS/CFT correspondence. Collective field theory performs a systematic reorganization of the degrees of freedom of a (non-gravitational) field theory, replacing the original loop expansion parameter $\hbar$ with $1/N$. Collective fields are over complete signalling a redundancy inherent in the theory. We propose that this over completeness is the mechanism by which one arrives at a holographic description, to be identified with the gravity dual. We find evidence for this by studying the redundancy of the collective field theory, showing that degrees of freedom in the bulk can be expressed as a linear combination of degrees of freedom contained in an arbitrarily small neighbourhood of the boundary.