Aspects of vacuum alignment

In the presence of both spontaneous symmetry breaking and explicit symmetry breaking, the ground state of a system is determined by vacuum alignment. In this thesis I examine the consequences of vacuum alignment in models with many competing explicit symmetry breaking interactions. In particular, I investigate the appearance of unexpectedly massless pseudo-Goldstone bosons and their connection to second order phase transitions in the symmetry of the ground state. The foundation for this investigation is a model based on the spontaneous symmetry breaking pattern SU(3)L ⊗ SU(3)R → SU(3).; One feature of this model, repeated phase transitions, motivates a new approach toward generating light states. In this approach, states are light because there are many nearby phase transitions rather than as a consequence of a symmetry. I test this new approach by applying repeated phase transitions to composite higgs models of electroweak symmetry breaking. This investigation not only elucidates the advantages and disadvantages of repeated phase transitions but it also provides a new path to a light composite higgs.; A more familiar approach to a light composite higgs is the Little Higgs mechanism. This achieves a light higgs by protecting it with additional global symmetries. As a consequence of these additional symmetries, new TeV scale particles must be introduced which tend to cause conflicts with precise low energy experiments. Imposing a discrete symmetry known as T parity on these models not only removes many problematic processes but also creates a dark matter candidate. I construct a T parity invariant version of the Simplest Little Higgs model and find a cosmologically viable dark matter candidate.; To demonstrate an application of vacuum alignment outside of electroweak symmetry breaking, I also examine the constraints from B meson mixings and decays on models of spontaneous CP violation in topcolor-assisted technicolor. In these models, CP is violated as a consequence of vacuum alignment in the technicolor sector, then communicated to the standard model fields through quark mass terms.