Factorization of 4d N=1 superconformal index

TL;DR

This paper demonstrates that the 4d N=1 superconformal index for certain gauge theories factorizes into vortex partition functions under specific conditions, and explores its relation to topological strings and 3D limits.

Contribution

It reveals the factorization of the superconformal index into elliptic vortex partition functions for U(N) theories with particular R-charge and vorticity conditions, linking to topological string theory.

Findings

Superconformal index factorizes into vortex partition functions.

Factorization holds under anomaly-free R-charge and traceless vorticity conditions.

3D limit reduces index to a factorized partition function on squashed sphere.

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.