Rigidly Supersymmetric Gauge Theories on Curved Superspace

Details Rigidly Supersymmetric Gauge Theories on Curved Superspace Rigidly Supersymmetric Gauge Theories on Curved Superspace

2011-09-26

arxiv.org/abs/1109.5421v3

Physics

High Energy Physics

High Energy Physics - Theory

23 pages; references added; more discussion added

Scientific paper

In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein four-manifolds such as AdS$_4$, N=1 rigidly supersymmetric sigma models are constrained to have target spaces with exact K\"ahler forms. Similarly, in gauged sigma models and gauge theories, we find that supersymmetry imposes constraints on Fayet-Iliopoulos parameters, which have the effect of enforcing that K\"ahler forms on quotient spaces be exact. We also discuss general aspects of universality classes of gauged sigma models, as encoded by stacks, and also discuss affine bundle structures implicit in these constructions.

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