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Title: Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory
Authors: Santilli, L.
Szabo, R. J.
Tierz, M.
Keywords: Field theories in higher dimensions
Field theories in lower dimensions
Supersymmetric gauge theory
Differential and algebraic geometry
Issue Date: 2020
Publisher: Springer
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 localiza- tion 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 de- scription 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 fur- ther 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).
Peer reviewed: yes
DOI: 10.1007/JHEP06(2020)036
ISSN: 1126-6708
Accession number: WOS:000540244700002
Appears in Collections:DM-RI - Artigos em revistas científicas internacionais

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