  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. In the second-type Chern-Simons-matter theory, the
partition function is related to integration over moduli space of Hitchin
equation on Riemann surface.
