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arXiv · 2606.03623

Twisted representations of conformal nets and crossed balanced tensor categories

Adrià Marín-Salvador
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Abstract

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

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Adrià Marín-Salvador. 2026-06-02. Twisted representations of conformal nets and crossed balanced tensor categories. https://arxiv.org/abs/2606.03623

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