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TMF, 2014, Volume 181, Number 1, Pages 86–120 (Mi tmf8648)  

This article is cited in 1 scientific paper (total in 1 paper)

Darboux coordinates, Yang–Yang functional, and gauge theory

N. A. Nekrasova, A. A. Roslyibc, S. L. Shatashvilidecfg

a Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, USA
b Institute for Theoretical and Experimental Physics, Moscow, Russia
c Institute for Theoretical and Experimental Physics, Moscow, Russia
d Euler International Mathematical Institute, St. Petersburg, Russia
e Louis Michel Chair, IHES, Bures-sur-Yvette
f The Hamilton Mathematics Institute, Trinity College, Dublin, Ireland
g School of Mathematics, Trinity College, Dublin, Ireland

Abstract: The moduli space of flat $SL_2$ connections on a punctured Riemann surface $\Sigma$ 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 $\mathcal{N}=2$ supersymmetric theory subject to the two-dimensional $\Omega$-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.

Keywords: gauge theory, supersymmetry, Hitchin integrable system, Darboux variable, quantization

DOI: https://doi.org/10.4213/tmf8648

Full text: PDF file (774 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 181:1, 1206–1234

Bibliographic databases:

Received: 01.02.2014

Citation: N. A. Nekrasov, A. A. Roslyi, S. L. Shatashvili, “Darboux coordinates, Yang–Yang functional, and gauge theory”, TMF, 181:1 (2014), 86–120; Theoret. and Math. Phys., 181:1 (2014), 1206–1234

Citation in format AMSBIB
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\paper Darboux coordinates, Yang--Yang functional, and gauge theory
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    Erratum

    This publication is cited in the following articles:
    1. Menotti P., “Classical conformal blocks”, Mod. Phys. Lett. A, 31:27 (2016), 1650159  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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