Proofs of some conjectures of Okazaki and Smith on line defect half-indices of $\mathrm{SU}(N)$ Chern-Simons theories

Liuquan Wang, Yiyang Yue

Okazaki and Smith discovered many elegant formulas expressing some matrix integrals as some celebrated $q$-series such as the Rogers--Ramanujan functions or Jacobi theta functions.…