N=1 Sigma Models in AdS_4

TL;DR

This paper investigates N=1 supersymmetric sigma models in AdS_4, revealing unique geometric constraints, vacuum structures, and implications for supergravity and string theory compactifications.

Contribution

It demonstrates that sigma models in AdS_4 require a Kahler manifold with an exact Kahler form and explores their role as limits of supergravity, highlighting novel geometric and physical features.

Findings

Target space must be a Kahler manifold with an exact Kahler form.

Supersymmetric vacua are typically isolated points even without superpotential.

AdS_4 scale masses are common in string compactifications, and AdS_4 regulates SQCD runaway behavior.

Abstract

We study sigma models in AdS_4 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 AdS_4 scale masses are ubiquitous in, for example, type IIB N=1 AdS_4 vacua stabilized near large volume; we also show that the Affleck-Dine-Seiberg runaway of N_f < N_c SQCD is regulated by considering the theory in AdS_4.