A Novel Spin-Statistics Theorem in (2 + 1)d Chern-Simons Gravity

TL;DR

This paper establishes a new spin-statistics theorem in (2+1)d Chern-Simons gravity, showing that despite violations of the canonical relation, statistics are fully determined by spin.

Contribution

It provides an algebraic framework demonstrating that in (2+1)d quantum gravity, statistics are uniquely determined by spin, even when the traditional spin-statistics connection fails.

Findings

Statistics are determined by spin in (2+1)d gravity.

The usual spin-statistics theorem does not hold in this context.

A new algebraic spin-statistics relation is formulated.

Abstract

It has been known for some time that topological geons in quantum gravity may lead to a complete violation of the canonical spin-statistics relation : there may exist no connection between spin and statistics for a pair of geons. We present an algebraic description of quantum gravity in (2 + 1)d based on the first order formalism of general relativity and show that, although the usual spin-statistics theorem is not valid, statistics is completely determined by spin. Hence, a new spin-statistics theorem can be formulated.