Manton's Exotic Vortex Equation

Abstract

In this paper, we study the equation which we call Manton's exotic vortex equation. The equation arose in Manton's study of a deformation of the classical vortex equation [Ma]. We first investigate the existence problem for Manton's exotic vortex equation and establish existence results. We then construct the moduli space of solutions. Finally, we establish a dimensional reduction for Manton's exotic vortex equation. More precisely, we establish a correspondence between solutions of Manton's exotic vortex equation and pseudo-Hermitian-Yang--Mills connections with pseudo-Hermitian metrics of signature (1,1).

56 pages, comments are welcome