Geometrical quantization of bosonic string with Wess-Zumino term on genus-g Riemann surface.

Abstract

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 $\ensuremath{\Sigma}$ and arrive at the conclusion that the curvature on a K\"ahler manifold is proportional to the central extension of Krichever and Novikov algebra on $\ensuremath{\Sigma}$ and vanishes at the critical dimension $d=26\ensuremath{-}\frac{(k{d}_{G})}{({C}_{V}+k)}$.