Representations of Conformal Nets Associated with Infinite-Dimensional Groups

Adamo MS, Giorgetti L, Tanimoto Y (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Journal of Lie Theory Heldermann Verlag

Book Volume: 35

Pages Range: 689-718

Journal Issue: 4

Abstract

We study the relation between representations of certain infinite-dimensional Lie groups and those of the associated conformal nets. For a chiral conformal net extending the net generated by the vacuum representation of a loop group or diffeomorphism group of the circle, we show that any conformal net representation induces a positive-energy representation of the corresponding group. Consequently, we prove that any representation of such a conformal net is automatically diffeomorphism covariant. Moreover, we show that the covariance cocycles of conformal net representations satisfy naturality with respect to the action of diffeomorphisms, i.e. the diffeomorphisms act equivariantly on the category of conformal net representations.

Authors with CRIS profile

Maria Stella Adamo Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Università degli Studi di Roma 'Tor Vergata' IT Italy (IT)

How to cite

APA:

Adamo, M.S., Giorgetti, L., & Tanimoto, Y. (2025). Representations of Conformal Nets Associated with Infinite-Dimensional Groups. Journal of Lie Theory, 35(4), 689-718.

MLA:

Adamo, Maria Stella, Luca Giorgetti, and Yoh Tanimoto. "Representations of Conformal Nets Associated with Infinite-Dimensional Groups." Journal of Lie Theory 35.4 (2025): 689-718.

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