3d Partition Function as Overlap of Wavefunctions

TL;DR

This paper computes the 3d N=4 theories' partition function on S^3 as an overlap of wavefunctions, linking it to boundary conditions and connecting with 4d superconformal index and 2d q-deformed Yang-Mills theory.

Contribution

It introduces a novel wavefunction overlap representation for the 3d partition function derived from 4d N=4 super Yang-Mills boundary conditions.

Findings

Partition function expressed as wavefunction overlap

Connection established with 4d superconformal index

Relation to 2d q-deformed Yang-Mills theory

Abstract

We compute the partition function on S^3 of 3d N=4 theories which arise as the low-energy limit of 4d N=4 super Yang-Mills theory on a segment or on a junction, and propose its 1d interpretation. We show that the partition function can be written as an overlap of wavefunctions determined by the boundary conditions. We also comment on the connection of our results with the 4d superconformal index and the 2d q-deformed Yang-Mills theory.