Infrared Divergences in Quantum Gravity and String Field Theory

Abstract

The main purpose of this thesis is to better understand how the Faddeev-Kulish method works in a theory that contains two massless gauge fields. We begin with a review of infrared divergences associated with soft particles. Subsequently, we consider as a model the Einstein-Maxwell theory coupled to a scalar field, for which the Lagrangian and the asymptotic potential are constructed. It turns out that theories, for which the cancellation of soft divergences with the Faddeev-Kulish method is already known, can be partially investigated within this model. The dressing of photon states with soft gravitons and the cancellation of the corresponding divergences, is studied as another partial case. The dressing of scalar asymptotic states with both soft gravitons and photons is studied as well, with some interesting features appearing at second and higher order corrections. On the contrary, we show that if hard photon legs are also included, the method seems to provide a series of possibly divergent operators that did not appear in the previous cases. We close with a discussion on how infrared divergences are realized in string theory and point some steps that might lead to the extension of the Faddeev-Kulish method within the framework of string field theory.