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Darboux coordinates, Yang-Yang functional, and gauge theory

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Abstract

The moduli space of flat SL 2 connections on a punctured Riemann surface Σ with fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates in which the generating function of the variety of SL 2 -opers is identified with the universal part of the effective twisted superpotential of the corresponding four-dimensional N=2 supersymmetric theory subject to the two-dimensional Ω-deformation. This allows defining the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group and relating it to the instanton counting of the four-dimensional gauge theories in the rank-one case.

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Authors and Affiliations

  1. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York, USA

    N. A. Nekrasov

  2. Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France

    N. A. Nekrasov

  3. Institute for Information Transmission Problems, Moscow, Russia

    N. A. Nekrasov, A. A. Rosly & S. L. Shatashvili

  4. Institute for Theoretical and Experimental Physics, Moscow, Russia

    N. A. Nekrasov & A. A. Rosly

  5. Hamilton Mathematics Institute, Trinity College, Dublin, Ireland

    S. L. Shatashvili

  6. School of Mathematics, Trinity College, Dublin, Ireland

    S. L. Shatashvili

  7. Louis Michel Chair, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France

    S. L. Shatashvili

  8. Euler International Mathematical Institute, St. Petersburg, Russia

    S. L. Shatashvili

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  1. N. A. Nekrasov
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Dedicated to L. D. Faddeev on the occasion of his 80th birthday

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Nekrasov, N.A., Rosly, A.A. & Shatashvili, S.L. Darboux coordinates, Yang-Yang functional, and gauge theory. Theor Math Phys 181, 1206–1234 (2014). https://doi.org/10.1007/s11232-014-0209-3

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