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) …

… Indeed this choice is the one that makes the zero, and first law of IH look just as the
corresponding laws of stationary black hole mechanics [ACK, Ashtekar-Beetle-Fairhurst-Krishnan]. …
We can model the IH system by a single SU(2) … The dof of the horizon are described in
terms of an SU(2) Chern-Simons theory with level k = …