Darboux coordinates, Yang-Yang functional, and gauge theory

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

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The moduli space of flat SL2 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 SL2-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.

Original languageEnglish
Pages (from-to)1206-1234
Number of pages29
JournalTheoretical and Mathematical Physics
Volume181
Issue number1
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Darboux variable
  • gauge theory
  • Hitchin integrable system
  • quantization
  • supersymmetry

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