On the reduction of 4d N=1 theories on S^2

TL;DR

This paper explores how four-dimensional N=1 gauge theories reduce to two dimensions on S^2, revealing how R-symmetry choices influence the resulting theories and their dualities.

Contribution

It provides a detailed analysis of the reduction process of N=1 theories on S^2 and connects R-symmetry choices to two-dimensional N=(0,2) gauge theories and dualities.

Findings

Reduction depends on background field couplings and R-symmetry.

Special R-symmetry choices yield N=(0,2) gauge theories.

Reductions imply new two-dimensional dualities.

Abstract

We discuss reductions of general N=1 four dimensional gauge theories on S^2. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that, for special choices of R-symmetry, the resulting two dimensional theory has a natural interpretation as an N=(0,2) gauge theory. As an application of our general observations, we discuss reductions of N=1 and N=2 dualities and argue that they imply certain two dimensional dualities.