Factorization of the 3d superconformal index with an adjoint matter

DOI10.1007/JHEP11(2015)028zbMATH Open1388.81674arXiv1506.03951MaRDI QIDQ2636074

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Publication date: 31 May 2018

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Abstract: We work out the factorization of the 3d superconformal index for N = 2 $U(N_c)$ gauge theory withone 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 N = 4 $U(N_c)$ theory with $N_f$ hypermultiplets at the index level. We explicitlyshow that monopole operators violating unitarity bound in a bad theory are mapped to free hypermultiplets in the dual side. For N = 2 $U(N_c)$ theory with one adjoint matter $X$, $N_f$ fundamental, $N_a$ anti-fundamental chiral multiplets with superpotential $W=tr{X}^{n+1}$, 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.

Full work available at URL: https://arxiv.org/abs/1506.03951

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