Super-Yang-Mills theories on S4 x R

TL;DR

This paper constructs super-Yang-Mills theories on various curved spaces like S4 x R and S4 x S1, providing foundational tools for studying 5d uplifts of 4d gauge theories derived from 6d (2,0) theories.

Contribution

It introduces methods to formulate maximal SYM theories on curved spaces such as S4 x R, S4 x S1, and S5 x R, including boundary couplings and conditions for placement on S^n x R.

Findings

Constructed super-Yang-Mills theories on S4 x R, S4 x S1, and S4 x interval.

Provided insights into 5d uplifts of gauge theories from 6d (2,0) theory.

Clarified conditions for placing SYM theories on S^n x R.

Abstract

We construct super-Yang-Mills theories on S4 x R, S4 x S1 and S4 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 S4, obtained by compactifying the 6d (2,0) theory. We pay special attention to the N=2* theory on S4. We also explain how to construct maximal SYM on S5 x R, and clarify when SYM theories can be put on S^n x R.