# Supersymmetric gauge theory on curved 7-branes

## TL;DR

This paper constructs new 7-dimensional supersymmetric gauge theories on curved spaces, incorporating a Chern-Simons-like term, by analyzing supersymmetry constraints for E7-branes without off-shell supergravity.

## Contribution

It introduces a novel method to derive supersymmetric gauge theories on curved 7-branes using G2-structures with intrinsic torsion, expanding the understanding of supersymmetry in curved backgrounds.

## Key findings

- Two classes of solutions with G2-structures were found.
- Explicit examples include theories on round and squashed S^7.
- Theories on S^3 x M_4 with hyperkähler M_4 were constructed.

## 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$^*$ 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 $M_4$ hyperk\"{a}hler.