N = 4 SYM on \Sigma \times S^2 and its Topological Reduction

TL;DR

This paper studies the twisted N=4 super Yang-Mills theory on a product space, showing how it reduces to a 2D theory when one factor shrinks, and computes correlation functions in the reduced model.

Contribution

It provides a detailed analysis of the topological reduction of N=4 SYM on  imes S^2 and calculates correlation functions in the resulting 2D theory.

Findings

Reduction of 4D N=4 SYM to 2D theory as S^2 shrinks

Explicit computation of BRST cohomology correlation functions

Insights into topological aspects of SYM on curved spaces

Abstract

We consider the twisted N = 4 SYM on \Sigma \times S^2. In the limit that S^2 shrinks to zero size the four dimensional theory reduces to a two dimensional SYM theory. We compute the correlation functions of a set of BRST cohomology classes in the reduced theory perturbed by mass.