Topological reduction of 4D SYM to 2D σ-models

1995/01/20 by M. Bershadsky, A. Johansen, Vladimir Sadov +2 · 8 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Geometry and complex manifolds #hep-th

paper · pdf · doi:10.1016/0550-3213(95)00242-k

published as Nucl.Phys. B448 (1995) 166-186 · 30 pages, harvmac

arxiv created 1995/01/20 · openalex publication_date 1995/08/01 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

Citations

• The Self-Duality Equations on a Riemann Surface
• Two Dimensional Gauge Theories Revisited
• On the cohomology ring of the moduli space of rank 2 vector bundles on a curve

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• Electric-magnetic duality and the geometric Langlands program
• Mirror symmetry, Langlands duality, and the Hitchin system
• Notes on theories with 16 supercharges
• The geometry of M5-branes and TQFTs