Generalized Seiberg-Witten equations on a Riemann surface. (English) Zbl 1386.57031

Dey, Rukmini; Thakre, Varun

J. Geom. Symmetry Phys. 45, 47-66 (2017).

Summary: In this paper we consider two-dimensionally reduced, generalized Seibert-Witten equations, defined on a compact Riemann surface. A novel feature of the reduction technique is that the resulting equations produce an extra “Higgs field”. Under suitable regularity assumptions, we show that the moduli space of gauge-equivalent classes of solutions to the reduced equations, is a smooth Kähler manifold and construct a pre-quantum line bundle over the moduli space of solutions.

MSC:

57R57	Applications of global analysis to structures on manifolds
53C26	Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53D50	Geometric quantization
35Q40	PDEs in connection with quantum mechanics

Keywords:

dimensional reduction; geometric quantization; Higgs field; hyper-Kähler manifolds; Seiberg-Witten equations