Holomorphic Blocks for 3d Non-abelian Partition Functions

TL;DR

This paper proves that the 3d N=2 gauge theory partition function can be constructed from a single holomorphic block, confirming a key conjecture in supersymmetric localization.

Contribution

It provides a rigorous proof that the partition functions of non-abelian 3d N=2 theories are assembled from holomorphic blocks, advancing understanding of supersymmetric field theories.

Findings

Exact computation of 3d partition functions

Verification of the holomorphic block conjecture for non-abelian theories

Enhanced understanding of supersymmetric localization in 3d gauge theories

Abstract

The most recent studies on the supersymmetric localization reveal many non-trivial features of supersymmetric field theories in diverse dimensions, and 3d gauge theory provides a typical example. It was conjectured that the index and the partition function of a 3d N=2 theory are constructed from a single component: the holomorphic block. We prove this conjecture for non-abelian gauge theories by computing exactly the 3d partition functions and holomorphic blocks.