Iterating free-field AdS/CFT: higher spin partition function relations

TL;DR

The paper establishes a simple relation between higher spin partition functions in AdS spaces of different dimensions, revealing an iterative structure in AdS/CFT correspondence that leads to trivial theories in certain cases.

Contribution

It introduces a novel iterative approach to AdS/CFT relating higher spin fields across dimensions, uncovering trivial conformal theories in specific cases.

Findings

Partition functions are related across dimensions via a simple formula.

Iterating AdS/CFT can produce trivial theories with zero degrees of freedom.

In 4D, the iteration yields a parity-even non-local conformal higher spin theory.

Abstract

We find a simple relation between a free higher spin field partition function on thermal quotient of AdS(d+1) and the partition function of the associated d-dimensional conformal higher spin field on thermal quotient of AdS(d). Starting with a conformal higher spin field defined on AdS(d) one may also associate to it another conformal field in d-1 dimensions, thus "iterating" AdS/CFT. We observe that in the case of d=4 this iteration leads to a "trivial" 3d higher spin conformal theory with parity-even non-local action: it describes zero total number of dynamical degrees of freedom and the corresponding partition function on thermal AdS(3) is equal to 1.