Topological Reduction of 4D SYM to 2D $σ$--Models

Details Topological Reduction of 4D SYM to 2D $σ$--Models Topological Reduction of 4D SYM to 2D $σ$--Models

1995-01-20

arxiv.org/abs/hep-th/9501096v1

Nucl.Phys. B448 (1995) 166-186

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, harvmac

Scientific paper

10.1016/0550-3213(95)00242-K

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 $\sigma$-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 $\sigma$-models on moduli space of solutions to Hitchin equations.

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