A novel spin-statistics theorem in (2+1)D Chern-Simons gravity

It has been known for some time that topological geons in quantum gravity m ay lead to a complete violation of the canonical spin-statistics relation: There may be no connection between spin and statistics for a pair of geons. We present an algebraic description of quantum gravity in a (2 + 1)D manif old of the form Sigma x R, based on the first-order canonical formalism of general relativity. We identify a certain algebra describing the system, an d obtain its irreducible representations. We then show that although the us ual spin-statistics theorem is not valid, statistics is completely determin ed by spin for each of these irreducible representations, provided one of t he labels of these representations, which we call flux, is superselected. W e argue that this is indeed the case. Hence, a new spin-statistics theorem can be formulated.