N = 1 sigma models in AdS[subscript 4]

Abstract

We study sigma models in AdS4 with global N = 1 supersymmetry and find that they differ significantly from their flat-space cousins — the target space is constrained to be a K¨ahler manifold with an exact K¨ahler form, the superpotential transforms under K¨ahler transformations, the space of supersymmetric vacua is generically a set of isolated points even when the superpotential vanishes, and the R-symmetry is classically broken by the cosmological constant. Remarkably, the exactness of the K¨ahler class is also required for the sigma model to arise as a decoupling limit of N = 1 supergravity, and ensures the vanishing of gravitational anomalies. As applications of these results, we argue that fields with AdS4 scale masses are ubiquitous in, for example, type IIB N = 1 AdS4 vacua stabilized near large volume; we also present a schematic argument that the Affleck-Dine- Seiberg runaway of Nf < Nc SQCD can be regulated by considering the theory in AdS4.