Factorization of 4d N=1 superconformal index

Abstract

We study the factorization of four dimensional N=1 superconformal index for U(N) (SU(N)) SQCD with N_F fundamental and anti-fundamental chiral multiplets. When both the anomaly free R-charge assignment and the traceless condition for total vorticities are satisfied, we find that the superconformal index factorizes to a pair of the elliptic uplift of the vortex partition functions. We also study the relation between open topological string and the the elliptic uplift of the vortex partition functions. In the three dimensional limit, we show index for U(N) theory reduces to the factorized form of the partition function on the three dimensional squashed sphere.

arXiv comment19 pages

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Cited by in corpus (16)

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• Localization on Hopf surfaces
• Gluing gravitational blocks for AdS black holes
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• Holomorphic blocks and the 5d AGT correspondence
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Supersymmetric index on T^2 x S^2 and elliptic genus
• Modularity of supersymmetric partition functions
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• Elliptic modular double and 4d partition functions
• Bootstrapping the $S^5$ partition function
• Reconstructing GKZ via topological recursion
• Proving the 6d Cardy Formula and Matching Global Gravitational Anomalies