Killing Spinors and SYM on Curved Spaces

TL;DR

This paper constructs new supersymmetric Yang-Mills theories on curved spaces with Killing spinors, introducing mass terms and Chern-Simons couplings, and analyzes their supersymmetry algebra and vacuum structure.

Contribution

It introduces two families of curved space SYM theories with modified supersymmetry, including mass and Chern-Simons terms, extending standard models to curved backgrounds.

Findings

Supersymmetry algebra includes curvature-dependent R-symmetry extensions.

Theories lack continuous Coulomb branches of maximally supersymmetric vacua.

Existence of a half-BPS Coulomb branch approaching flat space in the Ricci-flat limit.

Abstract

We construct two families of globally supersymmetric counterparts of standard Poincar\'e supersymmetric SYM theories on curved space-times admitting Killing spinors, in all dimensions less than six and eight respectively. The former differs from the standard theory only by mass terms for the fermions and scalars and modified supersymmetry transformation rules, the latter in addition has cubic Chern-Simons like couplings for the scalar fields. We partially calculate the supersymmetry algebra of these models, finding R-symmetry extensions proportional to the curvature. We also show that generically these theories have no continuous Coulomb branch of maximally supersymmetric vacua, but that there exists a half-BPS Coulomb branch approaching the standard Coulomb branch in the Ricciflat limit.