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

Black holes (BH’s) in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with punctures. Remarkably, when considering an ensemble of fixed horizon area a_H, the counting can be mapped to simply counting the number of SU(2) intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to a_H with logarithmic corrections ∆S=-(3)/(2)log⁡a_H. Our treatment from first principles settles previous controversies concerning the counting of states.