Loop Quantum Gravity meets Topological Phases of Matter at the Black Hole horizon

In this work we investigate the role played by large diffeomorphisms of quantum isolated horizons for the statistics of Loop Quantum Gravity black holes by means of their relation to the braid group. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum isolated horizon model of LQG based on SU(2)_k-Chern-Simons theory explicitly exhibits non-abelian anyonic statistics, since the quantum gravitational degrees of freedom of the horizon can be seen as flux-charge composites. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.