Table 2.

The CS-WZW correspondence after integrating over the gauge-fixing Lagrangian $\mathcal{L}$

Object in CS on $I\times \mathrm{\Sigma }$	Object in gauged WZW on $\mathrm{\Sigma }$
CS partition function $Z_{I\times \mathrm{\Sigma }}[{\mathsf{A}}_{\text{out}}^{1,0},{\mathsf{A}}_{\text{in}}^{0,1}]$	Gauged WZW partition function $Z_{\mathsf{A}}^{\text{WZW}}$
Expectation value W of n Wilson lines $\gamma =I\times \{z_i\}$ in rep. ${\rho }_1,\dots {\rho }_n$	Gauged WZW correlator ${⟨{\rho }_1(g(z_1))\cdots {\rho }_n(g(z_n))⟩}_{\mathsf{A}}$
$\mathrm{\Omega }$-cohomology with n Wilson lines	n-point space of conformal blocks