Complex symmetries, the SQCD vacuum and supersymmetric vacuum alignment

Abstract

The structure of the vacuum in supersymmetric QCD is investigated with particular emphasis on the role of complex global symmetries. The vacuum is shown to be characterised by a variety of condensates of the squark fields, and some subtle constraints on these, arising from chiral Ward identities for spontaneously broken symmetries, are derived. It is found that the whole vacuum degeneracy can be understood in terms of transformations in the complexification, G , of the global group G. However, in contrast to non-gauge theories the SQCD vacuum manifold is not the complex coset space G/ H ̃ , and the complex invariance group H̃ of the vacuum is not the complexification of a subgroup of G . These ideas are then used to give an improved discussion of the vacuum alignment problem in supersymmetric gauge theories entirely in terms of complex symmetries, and a simple technicolour model is presented which shows clearly that in supersymmetric theories even the nature of chiral symmetry breaking becomes a vacuum alignment problem.