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Santilli, L., Szabo, R. J. & Tierz, M. (2020). Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory. Journal of High Energy Physics. 2020 (6)
S. Leonardo et al., "Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory", in Journal of High Energy Physics, vol. 2020, no. 6, 2020
@article{leonardo2020_1714713855316, author = "Santilli, L. and Szabo, R. J. and Tierz, M.", title = "Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory", journal = "Journal of High Energy Physics", year = "2020", volume = "2020", number = "6", doi = "10.1007/JHEP06(2020)036" }
TY - JOUR TI - Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory T2 - Journal of High Energy Physics VL - 2020 IS - 6 AU - Santilli, L. AU - Szabo, R. J. AU - Tierz, M. PY - 2020 SN - 1126-6708 DO - 10.1007/JHEP06(2020)036 AB - 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). ER -