Wilson loops and free energies in 3D SYM: exact results, exponential asymptotics, and duality

Tierz, Miguel (Departamento de Matemática, Grupo de Física Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016 Lisboa, Portugal)

26 May 2019

Abstract: We show that 3D supersymmetric gauge theories on with massive fundamental hypermultiplets and with a Fayet–Iliopoulos (FI) term are solvable in terms of generalized Selberg integrals. Finite- expressions for the partition function and Wilson loop in arbitrary representations are given. We obtain explicit analytical expressions for Wilson loops with symmetric, antisymmetric, rectangular, and hook representations, in terms of Gamma functions of complex arguments. The free energy for the orthogonal and symplectic gauge groups is also given. The asymptotic expansion of the free energy is also presented, including a discussion of the appearance of exponentially small contributions. Duality checks of the analytical expressions for the partition functions are also carried out explicitly.


Published in: PTEP 2019 (2019) 053B01
Published by: Oxford University Press/Physical Society of Japan
DOI: 10.1093/ptep/ptz036
arXiv: 1804.10845
License: CC-BY-3.0



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