Supersymmetric gauge theory on curved 7-branes

Abstract

We construct novel $7d$ supersymmetric gauge theories which include a Chern-Simons-like term on curved spaces. In order to so, we examine the supersymmetry constraints for E7-branes in type IIA${}^{\ast }$ theory, rather than making use of an off-shell supergravity. We find two classes of solutions to the constraints, expressed in terms of a $G_2$-structure with non-vanishing intrinsic torsion. The supersymmetric gauge theories are then obtained by coupling flat gauge theory to such supersymmetric backgrounds. Various examples are given, including round and squashed $S^7$ as well as $S^3\times M_4$ with $M_4$ hyperkähler.

32 pages. v2: Added off-shell formulation. Updated references, minor corrections

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