Deformations, Symmetries and Topological Degrees of Freedom of the String

Abstract

We discuss three closely related questions; i)~Given a conformal field theory, how may we deform it? ii)~What are the symmetries of string theory? and iii)~Does string theory have free parameters? We show that there is a distinct deformation of the stress tensor for every solution to the linearised covariant equations of motion for the massless modes of the Bosonic string, and use this result to discuss the symmetries of the string. We also find an additional finite dimensional space of deformations which may correspond to free parameters of string theory, or alternatively may be interpreted as topological degrees of freedom, perhaps analogous to the isolated states found in two dimensions.