Theories Beyond the Worldline

Abstract

Standard quantum field theories usually have high energy divergences which render them unacceptable as a complete theory of nature. Such divergences arise from the nature of point particle excitations. This thesis looks to go beyond such frameworks. We begin by asking the general question: what possible modifications of point particle theories are there which might give them desirable properties such as finite and well-behaved amplitudes at high energies? We use the worldline formalism to construct modifications to worldline theories which have a tower of internal states propagating along the worldline, mimicking the behaviour of string oscillator modes. We argue that string theory itself can be regarded as a special case. We show that this class of theories shares similar interesting properties with string theory, and can also be used to analyse aspects of string theory itself. We then move on to focus on the phenomenology of string theory. We study a particular compactification of type I string theory, with the aim of constructing a model with a small but positive cosmological constant which has supersymmetry broken at a high scale. Such models usually suffer stability problems, but we will show that there is a class in which all moduli are either stabilised or flat up to exponentially suppressed terms. These models could be useful starting points for constructing either truly stabilised de Sitter minima, or perhaps as providing a quintessence scenario.