Non-abelian vortices on CP1 and Grassmannians

作者：Rink Norman A^*

来源：Journal of Mathematical Physics, 2013, 54(4): 043503.

DOI：10.1063/1.4798468

Many properties of the moduli space of abelian vortices on a compact Riemann surface Sigma are known. For non-abelian vortices the moduli space is less well understood. Here we consider non-abelian vortices on the Riemann sphere C P-1, and we study their moduli spaces near the Bradlow limit. We give an explicit description of the moduli space as a Kahler quotient of a finite-dimensional linear space. The dimensions of some of these moduli spaces are derived. Strikingly, there exist non-abelian vortex configurations on C P-1, with non-trivial vortex number, for which the moduli space is a point. This is in stark contrast to the moduli space of abelian vortices. For a special class of non-abelian vortices the moduli space is a Grassmannian, and the metric near the Bradlow limit is a natural generalization of the Fubini-Study metric on complex projective space. We use this metric to investigate the statistical mechanics of non-abelian vortices. The partition function is found to be analogous to the one for abelian vortices.

• 出版日期2013-4