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 language | English |
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Article number | 36 |
Journal | Journal of High Energy Physics |
Volume | 2020 |
Issue number | 6 |
DOIs | |
Publication status | Published - 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