A taxonomy of twists of supersymmetric Yang–Mills theory

Abstract

We give a complete classification of twists of supersymmetric Yang–Mills theories in dimensions \(2\le n \le 10\). We formulate supersymmetric Yang–Mills theory classically using the BV formalism, and then we construct an action of the supersymmetry algebra using the language of \(L_\infty \) algebras. For each orbit in the space of square-zero supercharges in the supersymmetry algebra, under the action of the spin group and the group of R-symmetries, we give a description of the corresponding twisted theory. These twists can be described in terms of mixed holomorphic-topological versions of Chern–Simons and BF theory.