Singletons in supersymmetric field theories and in supergravity

TL;DR

This paper investigates the role of singleton representations in N=1 supergravity with AdS boundary conditions, showing how relaxing boundary conditions allows singleton supermultiplets to appear and influence the boundary theory.

Contribution

It demonstrates the conditions under which singleton supermultiplets emerge in supergravity and their impact on holographic renormalization and boundary actions.

Findings

Singletons are absent under supersymmetry-preserving boundary conditions.

Relaxing boundary conditions allows singleton supermultiplets to appear.

Singletonic actions emerge in the boundary theory during holographic renormalization.

Abstract

We consider $N=1$ supergravity coupled to a Wess-Zumino multiplet with a potential such that the resulting AdS energies saturate the unitarity and Breitenlohner-Freedman bounds, respectively. Imposing regular boundary conditions that preserve supersymmetry and support finite norms, the spectrum forms an $OSp(1,4)$ supermultiplet in which the singleton representation is absent. We study the case in which this boundary condition is relaxed such that the singleton and its superpartners survive and form an indecomposable representation of $OSp(1,4)$. Focusing on the global limit of the model, we carry out its holographic renormalization, in which a singletonic action makes appearance in the boundary action.