Defect in Gauge Theory and Quantum Hall States

TL;DR

This paper explores the connection between surface defects in four-dimensional gauge theories and two-dimensional quantum Hall states, revealing that defect partition functions relate to Jack polynomials and can model various fractional quantum Hall states.

Contribution

It demonstrates that defect partition functions in $ ext{N}=2^*$ $U(N)$ gauge theory correspond to Jack polynomials and can reproduce multiple fractional quantum Hall states through parameter tuning.

Findings

Defect partition functions are Jack polynomials under certain conditions.

Tuning parameters yields Laughlin, Moore-Read, and Read-Rezayi states.

The work links gauge theory defects to quantum Hall phenomena.

Abstract

We study the surface defect in $\mathcal{N}=2^*$ $U(N)$ gauge theory in four dimensions and its relation to quantum Hall states in two dimensions. We first prove that the defect partition function becomes the Jack polynomial of the variables describing the brane positions by imposing the Higgsing condition and taking the bulk decoupling limit. Further tuning the adjoint mass parameter, we may obtain various fractional quantum Hall states, including Laughlin, Moore-Read, and Read-Rezayi states, due to the admissible condition of the Jack polynomial.