Deformations, Symmetries and Topological Degrees of Freedom of the String

TL;DR

This paper explores how conformal field theories can be deformed, investigates the symmetries of string theory, and examines the existence of free parameters or topological degrees of freedom within the theory.

Contribution

It establishes a link between deformations of the stress tensor and solutions to linearised equations of motion, and identifies a finite-dimensional space of potential free parameters or topological degrees of freedom.

Findings

Deformation of stress tensor corresponds to solutions of linearised equations.

Identifies a finite-dimensional space of deformations possibly representing free parameters.

Suggests these deformations may be analogous to topological degrees of freedom.

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.