Gauge/Bethe correspondence on $S^1 \times \Sigma_h$ and index over moduli space

Understand

We introduce two-types of topologically twisted Chern-Simons-matter theories on the direct product of circle and genus-h Riemann surface (S^1 \times \Sigma_h).

• The partition functions of first model agrees with the partition functions of a generalizations of G/G gauged WZW model.
• We also find that correlation functions of Wilson loops in first type Chern-Simons-matter theory coincide with correlation functions of G elements in the generalization of G/G gauged WZW model.
• The partition function of this model also has nice interpretations as norms of eigen states of Hamiltonian in the quantum integrable model (q-boson hopping model) and also as a geometric index over a particular moduli space.