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

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.

corrections in sections 3.1 and 3.3

References in corpus (3)

• A topologically twisted index for three-dimensional supersymmetric theories
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• A "Lagrangian" for a non-Lagrangian theory

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