Geometric quantization of the moduli space of the selfduality equations on a Riemann surface
Abstract
The selfduality equations on a Riemann surface arise as dimensional reduction of selfdual YangMills equations. Hitchin showed that the moduli space M of solutions of the selfduality equations on a compact Riemann surface of genus g > 1 has a hyperKähler structure. In particular M is a symplectic manifold. In this paper we elaborate on one of the symplectic structures, the details of which are missing in Hitchin's paper. Next we apply Quillen's determinant line bundle construction to show that M admits a prequantum line bundle. The Quillen curvature is shown to be proportional to the symplectic form mentioned above.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 April 2006
 DOI:
 10.1016/S00344877(06)800169
 arXiv:
 arXiv:mathph/0605026
 Bibcode:
 2006RpMP...57..179D
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Mathematical Physics;
 Mathematics  Symplectic Geometry
 EPrint:
 12 pages