The physical Hilbert space of complex Chern-Simons theory on an m-holed sphere at even level carries a Fenchel-Nielsen representation in which Wilson loops along pants-decomposition cuts act as multiplication operators.
The SU(2) Black Hole entropy revisited
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abstract
We study the state-counting problem that arises in the SU(2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU(2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important.
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Hamiltonian quantization of complex Chern-Simons theory at level-$k$
The physical Hilbert space of complex Chern-Simons theory on an m-holed sphere at even level carries a Fenchel-Nielsen representation in which Wilson loops along pants-decomposition cuts act as multiplication operators.