Super-Yang-Mills theories on S-4 x R

Abstract

We construct super-Yang-Mills theories on S-4 x R, S-4 x S-1 and S-4 x interval with the field content of maximal SYM, coupled to boundary degrees in the last case. These theories provide building blocks of the '5d uplifts' of gauge theories on S-4, obtained by compactifying the 6d (2, 0) theory. We pay special attention to the N = 2* theory on S-4. We also explain how to construct maximal SYM on S-5 x R, and clarify when SYM theories can be put on S-n x R.