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

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.