On the fermionic Grande Bouffe: more on higher spin symmetry breaking in AdS/CFT

TL;DR

This paper explores how fermionic higher spin gauge symmetries are spontaneously broken in AdS space, consistent with AdS/CFT correspondence, and identifies the Goldstino mode's mass and related currents.

Contribution

It extends the understanding of higher spin symmetry breaking to fermionic fields in AdS/CFT, providing explicit mass predictions and fermionic current structures.

Findings

Goldstino mode has non-zero mass when symmetry is broken

Higher spin symmetry enhancement occurs at zero coupling in N=4 SYM

Mass of Goldstino matches AdS/CFT predictions

Abstract

We discuss fermionic higher spin gauge symmetry breaking in AdS space from a holographic perspective. Analogously to the recently discussed bosonic case, the higher spin Goldstino mode responsible for the symmetry breaking has a non-vanishing mass in the limit in which the gauge symmetry is restored. This result is precisely in agreement with the AdS/CFT correspondence, which implies that N=4 SYM 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. We also show that the mass of the Goldstino mode is exactly the one predicted by the correspondence. Finally, we obtain the form of a class of fermionic higher spin currents in the SYM side.