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Prog. Theor. Phys. Supplement No.114 (1993) pp. 125-147

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Quantum Hilbert Space of GC Chern-Simons-Witten Theory and Gravity

Nobuharu Hayashi

Institute of Physics, University of Tokyo, Komaba, Tokyo 153

Abstract:

Euclidean Chern-Simons-Witten theory with a complex Lie group GC is discussed. When GC is a complexification of SU(2), this theory gives an important physical application. It describes Euclidean gravity with negative cosmological constant. In the present paper, we consider a quantum Hilbert space of the Chern-Simons-Witten theory with GC on a torus, and show that it is finite-dimensional at special values of coupling constants. In such cases, we find that any physical state is given by a product of the holomorphic Weyl-Kac character of the Wess-Zumino-Novikov-Witten model and the anti-holomorphic one. Moreover, it is also shown that each of topological invariants of 3-dimensional manifolds which admit the genus one Heegaard splitting is factorized into a product of two parts. One of them coincides with a topoligical invariant of the Chern-Simons-Witten theory with the maximal compact subgroup of GC and the other is closely related to its complex conjugate.


URL : http://ptp.ipap.jp/link?PTPS/114/125/
DOI : 10.1143/PTPS.114.125

[ Full Text PDF : FREE ACCESS (1677K) ] Citation:

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