An introduction to Riemann surfaces for physicists

Abstract

String theory with c ≤ 1 matter is described in the path-integral, conformal-gauge approach. It is shown how to obtain the gravitational scaling dimensions and string sus- ceptibility in this framework. This is followed by a discussion of the operator quantization of the theory, the nature of Liouville theory Fock space, the spectrum of physical states in the BRS framework, and the existence of extra physical states of nontrivial ghost number. Finally, I return to the path-integral to discuss the partition function on the torus and the tree-level correlation functions.