Chiral bosonization of superconformal ghosts on the Riemann surface and path-integral measure

Abstract

The bosonization of the bosonic ghosts β and γ using a pair of scalar fields φ and χ is formulated for the case of the Riemann surface with higher genus. The measure of the path integral over φχ fields is defined with a projector which specifies the picture of each loop and removes the zero-modes. Nevertheless, the resulting correlation functions are independent of the chosen pictures. The correspondence between the anomalous ghost number conservation laws and the Riemann-Roch theorem becomes also manifest. © 1989.