2006/05/08 by Rukmini Dey, Dey, Rukmini
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #hep-th #math-ph #math.MP #math.SG
paper · pdf · doi:10.48550/arxiv.math-ph/0605027
15 pages
openalex publication_date 2006/05/08 · arxiv created 2006/09/18 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Hitchin has shown that the moduli space \mathcal M of the dimensionally reduced self-dual Yang-Mills equations has a hyperKähler structure. In this paper we first explicitly show the hyperKähler structure, the details of which is missing in Hitchin's paper. We show here that \mathcal M admits three pre-quantum line bundles, corresponding to the three symplectic forms. We use Quillen's determinant line bundle construction and show that the Quillen curvatures of these prequantum line bundles are proportional to each of the symplectic forms mentioned above. The prequantum line bundles are holomorphic with respect to their respective complex structures. We show how these prequantum line bundles can be derived from cocycle line bundles of Chern-Simons gauge theory with complex gauge group in the case when the moduli space is smooth.