Factorization of the 3d superconformal index

Abstract

We prove that 3d superconformal index for general $\mathcal{N}=2$ U(N) gauge group with fundamentals and anti-fundmentals with/without Chern-Simons terms is factorized into vortex and anti-vortex partition function. We show that for simple cases, 3d vortex partition function coincides with a suitable topological open string partition function. We provide much more elegant derivation at the index level for $\mathcal{N}=2$ Seiberg-like dualities of unitary gauge groups with fundamantal matters and $\mathcal{N}=4$ mirror symmetry

43 pages, 2 figures ; minor revisions, some technical details clarified, add references

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• Quantum vortices, M2-branes and black holes
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• Factorization of 4d N=1 superconformal index
• Is toric duality a Seiberg-like duality in (2+1)-d ?
• Factorization of the 3d superconformal index with an adjoint matter