Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

Abstract

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact Kähler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, Kähler) structures ${\Omega }_{{\Psi }_0}$ on the moduli space, parametrised by ${\Psi }_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal{P}}_{{\Psi }_0}$on the moduli space whose curvature is proportional to the symplectic forms ${\Omega }_{{\Psi }_0}$.

8 pages

References in corpus (3)

• Vortex equations in abelian gauged sigma-models
• The Kähler Potential of Abelian Higgs Vortices
• Geometric quantization of the moduli space of the Self-duality equations on a Riemann surface

Cited by in corpus (1)

• Kähler quantization of vortex moduli