Defect in gauge theory and quantum Hall states

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