On the reduction of 4d N=1 theories on S2

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.