The classification of chiral WZW models by H4 +(BG, ℤ)

André Henriques

doi:10.1090/conm/695/13998

The classification of chiral WZW models by H⁴ ₊(BG, ℤ)

André Henriques^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

Abstract

We axiomatize the defining properties of chiral WZW models. We show that such models are in almost bijective correspondence with pairs (G, k), where G is a connected Lie group and k ∈ H⁴ ₊ (BG, ℤ) is a degree four cohomology class subject to a certain positivity condition. We find a couple extra models which satisfy all the defining properties of chiral WZW models, but which don’t come from pairs (G, k) as above. The simplest such model is the simple current extension of the affine VOA E₈ × E₈ at level (2, 2) by the group ℤ₂.

Original language	English
Title of host publication	Lie Algebras, Vertex Operator Algebras, and Related Topics
Subtitle of host publication	Proceedings of the Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras, Vertex Operator Algebras, and Related Topics August 14–18, 2015 University of Notre Dame, Notre Dame, IN
Editors	Katrina Barron, Elizabeth Jurisich, Antun Milas, Kailash Misra
Publisher	American Mathematical Society
Pages	99-121
Number of pages	23
ISBN (Electronic)	978-1-4704-4196-8
ISBN (Print)	978-1-4704-2666-8
DOIs	https://doi.org/10.1090/conm/695/13998
Publication status	Published - 2017

Publication series

Name	Contemporary Mathematics
Volume	695

Access to Document

10.1090/conm/695/13998

chiralFinal published version, 364 KBLicence: Taverne

Cite this

Henriques, A. (2017). The classification of chiral WZW models by H⁴ ₊(BG, ℤ). In K. Barron, E. Jurisich, A. Milas, & K. Misra (Eds.), Lie Algebras, Vertex Operator Algebras, and Related Topics: Proceedings of the Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras, Vertex Operator Algebras, and Related Topics August 14–18, 2015 University of Notre Dame, Notre Dame, IN (pp. 99-121). (Contemporary Mathematics; Vol. 695). American Mathematical Society. https://doi.org/10.1090/conm/695/13998

Henriques, André. / The classification of chiral WZW models by H⁴ ₊(BG, ℤ). Lie Algebras, Vertex Operator Algebras, and Related Topics: Proceedings of the Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras, Vertex Operator Algebras, and Related Topics August 14–18, 2015 University of Notre Dame, Notre Dame, IN. editor / Katrina Barron ; Elizabeth Jurisich ; Antun Milas ; Kailash Misra. American Mathematical Society, 2017. pp. 99-121 (Contemporary Mathematics).

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Henriques, A 2017, The classification of chiral WZW models by H⁴ ₊(BG, ℤ). in K Barron, E Jurisich, A Milas & K Misra (eds), Lie Algebras, Vertex Operator Algebras, and Related Topics: Proceedings of the Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras, Vertex Operator Algebras, and Related Topics August 14–18, 2015 University of Notre Dame, Notre Dame, IN. Contemporary Mathematics, vol. 695, American Mathematical Society, pp. 99-121. https://doi.org/10.1090/conm/695/13998

The classification of chiral WZW models by H⁴ ₊(BG, ℤ). / Henriques, André.
Lie Algebras, Vertex Operator Algebras, and Related Topics: Proceedings of the Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras, Vertex Operator Algebras, and Related Topics August 14–18, 2015 University of Notre Dame, Notre Dame, IN. ed. / Katrina Barron; Elizabeth Jurisich; Antun Milas; Kailash Misra. American Mathematical Society, 2017. p. 99-121 (Contemporary Mathematics; Vol. 695).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Henriques A. The classification of chiral WZW models by H⁴ ₊(BG, ℤ). In Barron K, Jurisich E, Milas A, Misra K, editors, Lie Algebras, Vertex Operator Algebras, and Related Topics: Proceedings of the Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras, Vertex Operator Algebras, and Related Topics August 14–18, 2015 University of Notre Dame, Notre Dame, IN. American Mathematical Society. 2017. p. 99-121. (Contemporary Mathematics). doi: 10.1090/conm/695/13998