# Braided categories of endomorphisms as invariants for local quantum field theories

December 07, 2015

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.

open access link
doi:10.1007/s00220-017-2937-3

@article{Giorgetti:2015jqa,
author = "Giorgetti, Luca and Rehren, Karl-Henning",
title = "{Braided categories of endomorphisms as invariants for
local quantum field theories}",
journal = "Commun. Math. Phys.",
volume = "357",
year = "2018",
number = "1",
pages = "3-41",
doi = "10.1007/s00220-017-2937-3",
eprint = "1512.01995",
archivePrefix = "arXiv",
primaryClass = "math.OA",
SLACcitation = "%%CITATION = ARXIV:1512.01995;%%"
}

Keywords:

*none*