Constructs Minkowskian Cardy CFTs from arbitrary conformal nets and proves three forms of Haag duality interpreted as modular invariance, Cardy consistency, and Morita equivalence.
Twisted representations of conformal nets and crossed balanced tensor categories
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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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2026 2verdicts
UNVERDICTED 2representative citing papers
Proves equivalence (Rep^G(A))^G ≅ Rep(A^G) as balanced W*-tensor categories for general (not necessarily rational) conformal nets A with faithful finite group G action, generalizing the rational case and including balances.
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Minkowskian open/closed conformal field theory possibly without vacuum: the Cardy case
Constructs Minkowskian Cardy CFTs from arbitrary conformal nets and proves three forms of Haag duality interpreted as modular invariance, Cardy consistency, and Morita equivalence.
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Proves equivalence (Rep^G(A))^G ≅ Rep(A^G) as balanced W*-tensor categories for general (not necessarily rational) conformal nets A with faithful finite group G action, generalizing the rational case and including balances.