The crossed braided tensor category of twisted and untwisted representations of the Heisenberg conformal net

2026/08/03 by Adrià Marín-Salvador
Mathematics · Physics and Astronomy · #hep-th #math.OA #math.QA #msc:81T40

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63 pages

Abstract

We show that the category of twisted/untwisted representations of the Heisenberg conformal net Heis is a continuous Tambara-Yamagami category for the group ℝ. We compute the associators and the ℤ/2-crossed braiding. By taking a ℤ/2-equivariantization, we obtain an explicit computation of the braided continuous tensor category of representations of the fixed-points conformal net Heis^ℤ/2. This provides the first explicit computation of a category of representations of a conformal net containing irreducible representations whose tensor product is a direct integral of irreducible representations.

Cited by

• Twisted representations of conformal nets and crossed balanced tensor categories
• Balanced tensor categories of representations of fixed-points conformal nets