Topological Reduction of 4D SYM to 2D σ--Models
M. Bershadsky, A. Johansen, V. Sadov, C. Vafa
Abstract
By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric σ-model in 2 dimensions. For N=2 SYM this maps Donaldson observables on products of two Riemann surfaces to quantum cohomology ring of moduli space of flat connections on a Riemann surface. For N=4 SYM it maps S-duality to T-duality for σ-models on moduli space of solutions to Hitchin equations.
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