Killing spinors and SYM on curved spaces

We construct two families of globally supersymmetric counterparts of standardPoincar\'e supersymmetric SYM theories on curved space-times admitting Killingspinors, in all dimensions less than six and eight respectively. The formerdiffers from the standard theory only by mass terms for the fermions andscalars and modified supersymmetry transformation rules, the latter in additionhas cubic Chern-Simons like couplings for the scalar fields. We partiallycalculate the supersymmetry algebra of these models, finding R-symmetryextensions proportional to the curvature. We also show that generically thesetheories have no continuous Coulomb branch of maximally supersymmetric vacua,but that there exists a half-BPS Coulomb branch approaching the standardCoulomb branch in the Ricciflat limit.Comment: 38 pages, LaTeX2e + JHEP.cls; v2: minor changes: corrected some typos, added one footnote and removed anothe