On Deformations of Conformal Field Theories

Recently, there has been substantial interest in mathematics in the conjectured moduli space of conformal field theories. The purpose of this paper is to investigate this space by what is known as perturbative methods. First, however, it is important to note that the moduli space itself is not yet well defined. There are different definitions of conformal field theory, for example the Segal approach [21, 11, 12] is quite substantially different from the vertex operator approach (see [14] and references therein). Since these definitions are not known to be equivalent, and their realizations are supposed to be points of the moduli space, the space itself therefore cannot be defined until a particular definition is selected.