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Black Hole Entropy and SU(2) Chern-Simons Theory

Abstract : We show that the isolated horizon boundary condition can be treated in a manifestly SU(2) invariant manner. The symplectic structure of gravity with the isolated horizon boundary condition has an SU(2) Chern-Simons symplectic structure contribution at the horizon with level k=a_H/ (4\pi \beta \ell^2_p). Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points (defects). In the large black hole limit quantum horizon degrees of freedom can be modelled by a single intertwiner. The coupling constant of the defects with the Chern Simons theory on the horizon is precisely given by the ratio of the area contribution of the defect to the macroscopic area a_H, namely \lambda= 16\pi^2 \beta \ell^2_p (j(j+1))^(1/2)/a_H.
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Contributor : Alejandro Perez <>
Submitted on : Thursday, June 4, 2009 - 9:05:22 PM
Last modification on : Saturday, April 11, 2020 - 2:09:42 AM

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Jonathan Engle, Karim Noui, Alejandro Perez. Black Hole Entropy and SU(2) Chern-Simons Theory. Physical Review Letters, American Physical Society, 2010, 105 (3), ⟨10.1103/PhysRevLett.105.031302⟩. ⟨hal-00391827⟩



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