Bi-Local Fields in AdS${}_5$ Spacetime

TL;DR

This paper explores the connection between bi-local fields in AdS${}_5$ spacetime and bi-local systems, revealing how their properties depend on brane location and providing insights into their role in higher-spin dualities.

Contribution

It establishes a relation between bi-local collective fields and bi-local systems in AdS${}_5$, showing how the effective spring constant varies with brane position.

Findings

The effective spring constant depends on the brane location.

A bi-local system with zero spring constant can be realized on the IR brane.

The study links bi-local fields to higher-spin gauge theories in AdS spacetime.

Abstract

Recently, the bi-local fields attract the interest in studying the duality between $O(N)$ vector model and a higher-spin gauge theory in AdS spacetime. In those theories, the bi-local fields are realized as collective one's of the $O(N)$ vector fields, which are the source of higher-spin bulk fields. Historically, the bi-local fields are introduced as a candidate of non-local fields by Yukawa. Today, Yukawa's bi-local fields are understood from a viewpoint of relativistic two-particle bound systems, the bi-local systems. We study the relation between the bi-local collective fields out of higher-spin bulk fields and the fields out of the bi-local systems embedded in AdS${}_5$ spacetime with warped metric. It is shown that the effective spring constant of the bi-local system depends on the brane, on which the bi-local system is located. In particular, a bi-local system with vanishing spring constant, which is similar to the bi-local collective fields, can be realized on a low-energy IR brane.