An explicit example of a moduli driven phase transition in heterotic models

Abstract

We present an explicit example of a gauge symmetry breaking phase transition in heterotic models, the dynamics of which are not thermal and can be described in a well controlled manner throughout. The phase transition is driven by the evolution of bundle moduli---moduli associated with gauge field vacuum expectation values in the hidden dimensions. We present the necessary parts of the four dimensional effective theory including moduli which describe the embedding of the gauge bundle within the gauge group. We then present exact cosmological solutions to the system before going on to use them to describe the phase transition. The explicit nature of our description enables us to plot how the gauge bosons associated with the symmetries which are broken in the transition gain masses with time. This is in contrast to the use, for example, of a brane collision as a modulus driven phase transition. In the course of this work we find a number of other interesting results. We observe that the K\"ahler potential of the system is given by the logarithm of the volume of the compact space even when bundle moduli are included. We also note that the dynamics of the gauge bundle mean that small instanton transitions are classically forbidden for all but a set of measure zero of the initial conditions of the system. The paper is written in such a manner that the cosmological description of the phase transition can be read independently of the derivation of the four dimensional theory.