Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory

Leonardo Santilli, Richard J. Szabo, Miguel Tierz

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Abstract

We revisit the duality between five-dimensional supersymmetric gauge theories and deformations of two-dimensional Yang-Mills theory from a new perspective. We give a unified treatment of supersymmetric gauge theories in three and five dimensions using cohomological localization techniques and the Atiyah-Singer index theorem. We survey various known results in a unified framework and provide simplified derivations of localization formulas, as well as various extensions including the case of irregular Seifert fibrations. We describe the reductions to four-dimensional gauge theories, and give an extensive description of the dual two-dimensional Yang-Mills theory when the three-dimensional part of the geometry is a squashed three-sphere, including its extension to non-zero area, and a detailed analysis of the resulting matrix model. The squashing parameter b yields a further deformation of the usual q-deformation of two-dimensional Yang-Mills theory, which for rational values b2 = p/s yields a new correspondence with Chern-Simons theory on lens spaces L(p, s).

Original languageEnglish
Article number36
JournalJournal of High Energy Physics
Volume2020
Issue number6
DOIs
Publication statusPublished - 4 Jun 2020

Keywords

  • Differential and Algebraic Geometry
  • Field Theories in Higher Dimensions
  • Field Theories in Lower Dimensions
  • Supersymmetric Gauge Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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