Existence and Stability of Spinning Embedded Vortices

I show the existence of a new type of vortex solution which is nonstatic but stationary and carries angular momentum. This spinning vortex can be embedded in models with trivial vacuum topology like a model with SU(2)global × U(1)local → U(1)global symmetry breaking. The stability properties of the embedded spinning vortex are also studied in detail and it is shown that stability improves drastically as angular momentum increases. The implications of this result for vortices embedded in the electroweak model are under study. E-mail address: [email protected] Also, Visiting Scientist, Department of Physics, Brown University, Providence, R.I. 02912. This work focuses on a new class of embedded vortices which are nonstatic but stationary and carry non-zero angular momentum. They may therefore be called spinning embedded vortices. It will be shown that these vortices have improved stability properties compared to their non-spinning counterparts (electroweak vortices with in a hypothetical model with Weinberg angle θw = π/2[1, 2, 3]) whose properties are discussed in the contributions of Klinkhamer and Vachaspati in this volume. Let’s first clarify the motivation for generalizing the concept of the nonspinning electroweak (hereafter EW) vortex. As is well known the vacuum manifold of the standard EW model is a three sphere S. This implies that the model does not support any stable topological defects. However, almost a couple of years ago, Vachaspati[2] pointed out that there is a vortex-like coherent state in the EW model which appears as an exact solution to the field equations. In a later paper[3] we showed that this coherent state, called the embedded electroweak vortex[4], is in fact stable for a finite sector in parameter space. We also showed that the stability sector does not include the physically realized values of parameters. This was unfortunate but raised an exciting new question: Are there different types of embedded vortices with improved stability properties?. Until recently there had been two main classes of attempts to address this question. The first class originated from a work of Vachaspati and Watkins[5] who showed that bound states on the embedded vortex may indeed improve its stability. Due to the complexity of the problem however, it was not clear if this improvement of stability was enough to stabilize the electroweak vortex for the physical values of parameters. The second class focused on embeddings in extensions of the standard EW model. There have been several interesting works on this subject[6, 7, 8, 9] but of particular interest is the work of Dvali and Senjanovic[8] who discovered topologically stable vortices in the two Higgs doublet EW model. Here I focus on a new stabilization mechanism which is applicable to vortices of the standard, minimal EW model and introduces spin to improve the stability of the embedded vortices. An efficient way to introduce angular momentum to the vortex configuration is to embed it in a background of charge density which may be provided for example, by a charged external field with coherence length much larger than the width of the vortex. Consider a toy model with symmetry breaking SU(2)global×U(1)local −→ U(1)global. For our purpose, this model is identical to the bosonic sector of the