Braided categories of endomorphisms as invariants for local quantum field theories

TL;DR

This paper introduces a braided action of the DHR category as a complete, model-independent invariant for classifying completely rational chiral conformal quantum field theories, capturing full dynamical information without relying on the vacuum state.

Contribution

It defines the braided action of the DHR category as a new invariant that fully characterizes chiral CFTs, extending beyond traditional invariants.

Findings

Braided action encodes full dynamical information.

Geometric properties of duality pairing are established.

Under certain assumptions, the braided action classifies models completely.

Abstract

We want to establish the "braided action" (defined in the paper) of the DHR category on a universal environment algebra as a complete invariant for completely rational chiral conformal quantum field theories. The environment algebra can either be a single local algebra, or the quasilocal algebra, both of which are model-independent up to isomorphism. The DHR category as an abstract structure is captured by finitely many data (superselection sectors, fusion, and braiding), whereas its braided action encodes the full dynamical information that distinguishes models with isomorphic DHR categories. We show some geometric properties of the "duality pairing" between local algebras and the DHR category which are valid in general (completely rational) chiral CFTs. Under some additional assumptions whose status remains to be settled, the braided action of its DHR category completely classifies a (prime) CFT. The approach does not refer to the vacuum representation, or the knowledge of the vacuum state.