Abstract
We investigate an \( \mathcal{N} = 4\;\mathrm{U}{(N)}_k\times \mathrm{U}{\left(N+M\right)}_{-k} \) Chern-Simons theory coupled to one bifundamental hypermultiplet by employing its partition function, which is given by 2N + M dimensional integration via localization. Surprisingly, by performing the integration explicitly we find that the partition function completely factorizes into that of the pure Chern-Simons theory for two gauge groups and an analogous contribution for the bifundamental hypermultiplet. Using the factorized form of the partition function we argue the level/rank duality, which is also expected from the Hanany-Witten transition in the type IIB brane realization. We also present the all order ’t Hooft expansion of the partition function and comment on the connection to the higher-spin theory.
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Nosaka, T., Yokoyama, S. Complete factorization in minimal \( \mathcal{N}=4 \) Chern-Simons-matter theory. J. High Energ. Phys. 2018, 1 (2018). https://doi.org/10.1007/JHEP01(2018)001
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DOI: https://doi.org/10.1007/JHEP01(2018)001