Twisted traces and quantization of moduli stacks of 3d $\mathcal{N}=4$ Chern-Simons-matter theories

TL;DR

This paper explores the relationship between sphere partition functions of 3d $ =4$ Chern-Simons-matter theories and twisted traces on quantized moduli spaces, extending existing conjectures and revealing new dualities.

Contribution

It extends the Gaiotto-Okazaki conjecture to Chern-Simons-matter theories and demonstrates twisted trace decompositions for Abelian gauge theories with higher charges.

Findings

Sphere partition functions equal sums of twisted traces on quantized moduli spaces.

Extension of Gaiotto-Okazaki conjecture to Chern-Simons-matter theories.

Discovery of new Abelian dualities involving Chern-Simons couplings.

Abstract

We conjecture, and show in a plethora of examples, that the sphere partition function of 3d $\mathcal{N}=4$ Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua. This extends a conjecture of Gaiotto-Okazaki to Chern-Simons-matter theories. We also show that the partition function of every Abelian gauge theory with higher charges has such twisted trace decomposition, and uncover new Abelian dualities between theories with and without Chern-Simons couplings.