Abstract
We find boundary confining dualities of 3d \( \mathcal{N} \) = 2 supersymmetric gauge theories with exceptional gauge groups. The half-indices which enumerate the boundary BPS local operators in the presence of Neumann and Dirichlet boundary conditions for gauge fields are identified with the Askey-Wilson type q-beta integrals and Macdonald type sums respectively. New conjectural identities of E6 and E7 integrals and sums are derived from the boundary confining dualities. We also consider theories with a vector multiplet and adjoint chiral, which correspond to an \( \mathcal{N} \) = 4 vector multiplet, with appropriate boundary conditions. We argue for the boundary confinement of the \( \mathcal{N} \) = 4 vector multiplet and comment on such theories also with classical gauge groups.
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Acknowledgments
The authors would like to thank Masahiko Ito and Masatoshi Noumi for useful discussions and comments. The work of T.O. was supported by the Startup Funding no. 4007012317 of the Southeast University. The research of DJS was supported in part by the STFC Consolidated grant ST/T000708/1.
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Okazaki, T., Smith, D.J. 3d exceptional gauge theories and boundary confinement. J. High Energ. Phys. 2023, 199 (2023). https://doi.org/10.1007/JHEP11(2023)199
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DOI: https://doi.org/10.1007/JHEP11(2023)199