String Theory: exact solutions, marginal deformations and hyperbolic spaces

TL;DR

This thesis explores string theory backgrounds with simple geometries, focusing on Wess-Zumino-Witten models, marginal deformations, and hyperbolic spaces, providing insights into their moduli space, off-shell behavior, and solutions with Ramond-Ramond fields.

Contribution

It offers a detailed analysis of marginal deformations in WZW models, including asymmetric cases, and investigates solutions involving hyperbolic spaces with Ramond-Ramond fields.

Findings

Characterization of the moduli space via marginal deformations

Description of off-shell relaxation towards equilibrium

Identification of solutions with hyperbolic spaces in string backgrounds

Abstract

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces.