Abstract
We work out the factorization of the 3d superconformal index for \( \mathcal{N}=2 \) U(N c ) gauge theory with one adjoint chiral multiplet as well as N f fundamental, N a anti-fundamental chiral multiplets. Using the factorization, one can prove the Seiberg-like duality for \( \mathcal{N}=4 \) U(N c ) theory with N f hypermultiplets at the index level. We explicitly show that monopole operators violating unitarity bound in a bad theory are mapped to free hypermultiplets in the dual side. For \( \mathcal{N}=2 \) U(N c ) theory with one adjoint matter X, N f fundamental, N a anti-fundamental chiral multiplets with superpotential W = trX n+1, we work out Seiberg-like duality for this theory. The index computation provides combinatorial identities for a dual pair, which we carry out intensive numerical checks.
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Hwang, C., Park, J. Factorization of the 3d superconformal index with an adjoint matter. J. High Energ. Phys. 2015, 28 (2015). https://doi.org/10.1007/JHEP11(2015)028
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DOI: https://doi.org/10.1007/JHEP11(2015)028