More on La Grande Bouffe: towards higher spin symmetry breaking in AdS

TL;DR

This work analyzes higher spin symmetry breaking in AdS from a holographic viewpoint, showing that in the AdS bulk the Goldstone mode associated with restoring HS gauge symmetry is itself massive, with its mass precisely fixed by the AdS/CFT correspondence. By examining spins 1, 2, and general spin-s fields, the authors demonstrate that in AdS a massive spin-s field generically decomposes in the zero-mass limit into a massless spin-s plus a massive spin-(s−1), with the AdS mass terms agreeing with boundary operator dimensions. They provide a superspace formulation of HS multiplets in N=4 SYM, detailing how interactions convert HS current multiplets into long multiplets via anomalies, including the Konishi case. The results connect the bulk Higgs mechanism to boundary current nonconservation, align with DESWALD’s partial masslessness, and outline future directions toward mixed-symmetry tensors and Vasiliev-type formulations. Overall, the paper clarifies the structure and constraints of HS symmetry breaking in holography, with implications for HS dynamics and deconfinement in AdS/CFT.

Abstract

We discuss higher spin gauge symmetry breaking in AdS space from a holographic prespective. Indeed, the AdS/CFT correspondence implies that N=4 SYM theory at vanishing coupling constant is dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, the current conservation condition becomes anomalous, and correspondingly the local higher spin symmetry in the bulk gets spontaneously broken. In agreement with previous results and holographic expectations, we find that the Goldstone mode responsible for the symmetry breaking in AdS has a non-vanishing mass even in the limit in which the gauge symmetry is restored. Moreover, we show that the mass of the Goldstone mode is exactly the one predicted by the correspondence. Finally, we obtain the precise form of the higher spin supercurrents in the SYM side.