String Field Theory for Nontrivial Backgrounds

Abstract

In this thesis, we explore the application of (classical) string field theory (SFT) to the study of a variety of string theory backgrounds, which are described at the worldsheet level by two-dimensional conformal field theories (CFTs). As string theory is a theory of quantum gravity, different spacetime backgrounds are viewed as dynamical solutions to the equations of motion, and SFT provides a framework to perturbatively study these solutions beyond what is possible from on-shell string theory amplitudes. We begin with open string field theory (OSFT) and the study of time-dependent backgrounds, reviving the covariant phase space method to study the energy of the rolling tachyon, both analytically and through level truncation. We find a match between the pure-OSFT energy and the value previously known from open-closed SFT. Along the way we also present an application of the conformal bootstrap to the study of the boundary CFT describing the rolling tachyon. We then proceed to closed string field theory (CSFT) and develop a formalism for using it as a natural organizing framework in the study of deformations of conformal field theories. The flat string vertex is introduced as a key simplifying tool for these calculations, and the relationship between the free boson and minimal model CFTs is explored. We continue with this technology to explore how diffeomorphism symmetry manifests in SFT, allowing us to demonstrate SFT solutions that describe a change in topology of the background.