N=1 Sigma Models in AdS_4

TL;DR

This work analyzes N=1 sigma models in AdS$_4$, showing that the combination of supersymmetry and AdS curvature forces the target space to be a Kahler manifold with an exact Kahler form and that the superpotential must transform under Kahler transformations. Consequently, supersymmetric vacua are generically isolated with scalar masses tied to the AdS scale, and there are no mixed gravitational anomalies when coupled to supergravity, consistent with a decoupling limit from supergravity. The authors connect these rigid AdS$_4$ constraints to moduli stabilization in string compactifications and to the regulation of the ADS runaway in SQCD by AdS curvature, arguing for a broader Background Principle linking flat-space UV completions to AdS$_4$ consistency. Collectively, the results imply that AdS$_4$ backgrounds impart robust, model-independent constraints on the geometry of sigma models and on low-energy moduli and dynamics in supersymmetric theories. These insights illuminate why light moduli persist in large-volume AdS$_4$ compactifications and offer a controlled setting to study nonperturbative effects and gauge dynamics in curved backgrounds.

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.