  A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on
a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry
arises at each puncture inducing an infinite set of new observables localized
at the horizon which satisfy a Kac-Moody algebra. By means of the isolated
horizon boundary conditions, we represent the gravitational fluxes degrees of
freedom in terms of the zero modes of the Kac-Moody algebra defined on the
boundary of a punctured disk. In this way, our construction encodes a precise
notion of CFT/gravity correspondence. The higher modes in the algebra represent
new nongeometric charges which can be represented in terms of free matter field
degrees of freedom. When computing the CFT partition function of the system,
these new states induce an extra degeneracy factor, representing the density of
horizon states at a given energy level, which reproduces the Bekenstein's
holographic bound for an imaginary Immirzi parameter. This allows us to recover
the Bekenstein-Hawking entropy formula without the large quantum gravity
corrections associated with the number of punctures.
