Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 6, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP06(2020)036
Keywords
Field Theories in Higher Dimensions; Field Theories in Lower Dimensions; Supersymmetric Gauge Theory; Differential and Algebraic Geometry
Categories
Funding
- Fundacao para a Ciencia e a Tecnologia (FCT) [SFRH/BD/129405/2017]
- FCT [PTDC/MAT-PUR/30234/2017]
- U.K. Science and Technology Facilities Council (STFC) [ST/P000363/1]
- Fundação para a Ciência e a Tecnologia [SFRH/BD/129405/2017] Funding Source: FCT
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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 b(2) = p/s yields a new correspondence with Chern-Simons theory on lens spaces L(p, s).
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