Some comments on Chern-Simons gauge theory |
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| Authors: | Ramadas T R Singer I M Weitsman J |
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| Institution: | (1) Department of Mathematics, M.I.T., 02139 Cambridge, MA, USA;(2) Present address: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005 Bombay, India |
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| Abstract: | Following M. F. Atiyah and R. Bott AB] and E. Witten W], we consider the space of flat connections on the trivialSU(2) bundle over a surfaceM, modulo the space of gauge transformations. We describe on this quotient space a natural hermitian line-bundle with connection and prove that if the surfaceM is now endowed with a complex structure, this line bundle is isomorphic to the determinant bundle. We show heuristically how path-integral quantisation of the Chern-Simons action yields holomorphic sections of this bundle.I.M.S. and T.R.R. supported by DOE grant DE-FG02-88ER 25066. J.W. supported by NSF Mathematical Sciences post-doctoral research scholarship 8807291 |
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