Defect in gauge theory and quantum Hall states

We study the surface defect in 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.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

In this study, we investigate the surface defect in N = 2* U(N) gauge theory in four dimensions and its connection to quantum Hall states in two dimensions. We demonstrate that the defect partition function can be represented by the Jack polynomial of the variables describing the brane positions by imposing the Higgsing condition and taking the bulk decoupling limit. By further adjusting the adjoint mass parameter, different fractional quantum Hall states, such as Laughlin, Moore-Read, and Read-Rezayi states, can be obtained based on the admissible condition of the Jack polynomial.