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arXiv · 1912.10682

Bisognano-Wichmann property for rigid categorical extensions and non-local extensions of conformal nets

Bin Gui
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Abstract

Given an (irreducible) Mobius covariant net $\mathcal A$, we prove a Bisognano-Wichmann theorem for its categorical extension $\mathscr E^{\textrm{d}}$ associated to the braided $C^*$-tensor category $\textrm{Rep}^{\textrm{d}}(\mathcal A)$ of dualizable (more precisely "dualized") Mobius covariant $\mathcal A$-modules. As a closely related result, we prove a (modified) Bisognano-Wichmann theorem for any (possibly) non-local extension of $\mathcal A$ obtained by a $C^*$-Frobenius algebra $Q$ in $\textrm{Rep}^{\textrm{d}}(\mathcal A)$. As an application, we discuss the relation between the domains of modular operators and the preclosedness of certain unbounded operators in $\mathscr E^{\textrm{d}}$.

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BibTeXRIS

Bin Gui. 2019-12-23. Bisognano-Wichmann property for rigid categorical extensions and non-local extensions of conformal nets. https://doi.org/10.1007/s00023-021-01078-5

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