A taxonomy of twists of supersymmetric Yang-Mills theory

We give a complete classification of twists of supersymmetric Yang-Mills theories in dimensions 2 <= n <= 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-infinity 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.