Balanced tensor categories of representations of fixed-points conformal nets

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

paper · pdf

50 pages, references updated

arxiv created 2026/08/04 · arxiv updated 2026/08/06

Abstract

Let A be a (not necessarily rational) conformal net with a faithful action of a finite group G. Let Rep^G(A) be the G-crossed balanced W^*-tensor category of G-twisted representations of A as introduced in arXiv:2606.03623. We show that there is an equivalence of balanced W^*-tensor categories (Rep^G(A))^G≅ Rep(A^G) between the G-equivariantization of Rep^G(A) and the category of representations of the fixed-points conformal net A^G. This generalizes to the non-rational case the equivalence of braided tensor categories (Rep^G(A))^G≅ Rep(A^G) for A rational appearing (in the language of localized endomorphisms) in arXiv:math/0403322, and it also includes the balances.

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