Massive higher spins and holography

TL;DR

This paper reviews how higher spin gauge symmetries in AdS space are broken via holography, connecting the behavior of SYM theory at different couplings to the mass and symmetry properties of bulk fields.

Contribution

It provides a detailed holographic analysis of higher spin symmetry breaking, including the mass spectrum of Goldstone modes and their relation to gauge symmetry restoration.

Findings

Goldstone modes generally have non-zero mass even when symmetry is restored

Spontaneous symmetry breaking follows a Stueckelberg mechanism with predictable mass relations

Exception for spin 1, which can be eaten by spin 0

Abstract

We review recent progress towards the understanding of higher spin gauge symmetry breaking in AdS space from a holographic vantage point. According to the AdS/CFT correspondence, N=4 SYM theory at vanishing coupling constant should be dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, all but a handful of HS currents are violated by anomalies, and correspondingly local higher spin symmetry in the bulk gets spontaneously broken. In agreement with previous results and holographic expectations, we find that, barring one notable exception (spin 1 eating spin 0), the Goldstone modes responsible for HS symmetry breaking in AdS have non-vanishing mass even in the limit in which the gauge symmetry is restored. We show that spontaneous breaking a' la Stueckelberg implies that the mass of the relevant spin s'=s-1 Goldstone field is exactly the one predicted by the correspondence.