Geometrical quantization of bosonic string with Wess-Zumino term on genus-gRiemann surface

By combining the method of geometrical quantization and Krichever and Novikov algebra, we study the holomorphic structure of a bosonic string with Wess-Zumino term on a genus-$g$ Riemann surface $\Sigma$ and arrive at the conclusion that the curvature on a Kähler manifold is proportional to the central extension of Krichever and Novikov algebra on $\Sigma$ and vanishes at the critical dimension $d=26-\frac{\left(k{d}_G\right)}{(C_V+k)}$.