The Conformal Spin and Statistics Theorem

TL;DR

This paper proves a fundamental equality in Conformal Quantum Field Theory relating the statistics phase to conformal univalence for sectors with finite index, and discusses PCT symmetry and conjugate charges.

Contribution

It establishes the equality between the statistics phase and conformal univalence for finite index sectors, providing insights into PCT symmetry and charge conjugation.

Findings

Proves the equality between statistics phase and conformal univalence.

Provides a description of PCT symmetry in this context.

Constructs the global conjugate charge for sectors with finite index.

Abstract

We prove the equality between the statistics phase and the conformal univalence for a superselection sector with finite index in Conformal Quantum Field Theory on $S^1$. A relevant point is the description of the PCT symmetry and the construction of the global conjugate charge.