ABSTRACT
Conformal field theory is a two-dimensional quantum field theory defined over compact Riemann surfaces. It was initiated by Belavin, Polyakov and Zamolodchikov [4]. The theory is invariant under conformal transformations. Since the group of conformal transformations is of infinite dimension, conformal field theory is reduced to finite degrees of freedom by the conformal invariance. It is well-known that an oriented surface S with a Riemannian metric determines a complex structure. Moreover, the complex structure is uniquely determined by the conformal class of the metric.
