Algebraic structures in two-dimensional conformal field theory

Fuchs, Jürgen, Schweigert, Christoph, Wood, Simon ORCID: https://orcid.org/0000-0002-8257-0378 and Yang, Yang 2024. Algebraic structures in two-dimensional conformal field theory. Szabo, Richard, Bojowald, Martin and Meusburger, Catherine, eds. Encyclopedia of Mathematical Physics (Second Edition), Vol. 3. Elsevier, pp. 604-617. (10.1016/B978-0-323-95703-8.00013-6)

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Abstract

The symmetries of two-dimensional conformal field theories (CFTs) can be formalised as chiral algebras, vertex operator algebras or nets of observable algebras. Their representation categories are abelian categories having additional structures. These structures are induced by properties of conformal blocks, i.e. of vector bundles over the moduli space of curves with marked points, which can be constructed from the symmetry structure. These mathematical notions pertain to the description of chiral CFTs. In a full local CFT one deals in addition with correlators, which are specific elements in the spaces of conformal blocks. In fact, a full CFT is the same as a consistent system of correlators for arbitrary conformal surfaces with any number and type of field insertions in the bulk as well as on boundaries and on topological defect lines. We present algebraic structures that allow one to construct such systems of correlators.

Item Type:	Book Section
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Elsevier
ISBN:	9780323957069
Funders:	EPSRC
Date of First Compliant Deposit:	19 March 2025
Date of Acceptance:	3 September 2023
Last Modified:	25 Mar 2025 12:30
URI:	https://orca.cardiff.ac.uk/id/eprint/176995

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