Twisted representations of conformal nets and crossed balanced tensor categories

2026/06/30 by Adrià Marín-Salvador · 2 citations
Mathematics · Physics and Astronomy · #math.QA #math-ph #math.MP #math.OA #msc:81T40

paper · pdf

49 pages, references updated

arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

Let A be a (not necessarily rational) conformal net with an action of a discrete group G. We show that the category Rep^G(A) of G-twisted representations of A is canonically a G-crossed balanced W^*-tensor category. This extends the results of Müger arXiv:math/0403322, in the language of localized endomorphisms, that Rep^G(A) is a G-crossed braided tensor category.

Citations

• The crossed braided tensor category of twisted and untwisted representations of the Heisenberg conformal net
• Representations of fusion categories and their commutants
• Loop groups and diffeomorphism groups of the circle as colimits
• Bicommutant categories from conformal nets
• Conformal nets I: coordinate-free nets
• On braided fusion categories I
• On braided fusion categories I
• Conformal covariance and related properties of chiral QFT
• Classification of Local Conformal Nets. Case c < 1
• Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
• Operator Algebras and Conformal Field Theory III. Fusion of positive energy representations of LSU(N) using bounded operators
• Operator algebras and conformal field theory
• The Conformal Spin and Statistics Theorem
• Modular structure and duality in conformal quantum field theory
• On Unitary Ray Representations of Continuous Groups
• Conformal Orbifold Theories and Braided Crossed G-Categories

Cited by

• Balanced tensor categories of representations of fixed-points conformal nets