N=1 Sigma Models in AdS4
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 Kahler manifold with an exact Kahler form, the superpotential transforms under Kahler 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 Kahler 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 simple 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 show that the Affleck-Dine-Seiberg runaway of Nf < Nc SQCD is regulated by considering the theory in AdS4.