Bordism for the 2-group symmetries of the heterotic and CHL strings

Arun Debray

doi:10.1090/conm/802/16079

Bordism for the 2-group symmetries of the heterotic and CHL strings

Arun Debray

Mathematics

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

12 Scopus citations

Abstract

In the presence of a nonzero B-field, the symmetries of the E8×E8 heterotic string form a 2-group, or a categorified group, as do the symmetries of the CHL string. We express the bordism groups of the corresponding tangential structures as twisted string bordism groups, then compute them through dimension 11 modulo a few unresolved ambiguities. Then, we use these bordism groups to study anomalies and defects for these two string theories.

Original language	English
Title of host publication	Higher Structures in Topology, Geometry, and Physics - AMS Special Session Higher Structures in Topology, Geometry, and Physics, 2022
Editors	Ralph M. Kaufmann, Martin Markl, Alexander A. Voronov
Pages	227-297
Number of pages	71
DOIs	https://doi.org/10.1090/conm/802/16079
State	Published - 2024
Event	AMS Special Session on Higher Structures in Topology, Geometry, and Physics, 2022 - Virtual, Online Duration: Mar 26 2022 → Mar 27 2022

Publication series

Name	Contemporary Mathematics
Volume	802
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Conference

Conference	AMS Special Session on Higher Structures in Topology, Geometry, and Physics, 2022
City	Virtual, Online
Period	3/26/22 → 3/27/22

Bibliographical note

Publisher Copyright:
© 2024 American Mathematical Society.

Funding

I especially want to thank Miguel Montero both for suggesting this project and for many helpful conversations about the material in this paper, and Matthew Yu for many helpful discussions relating to [DY23] and other ideas related to this paper. I also want to thank Markus Dierigl and the anonymous referee for helpful comments on a draft. In addition, this paper benefited from conversations with Ivano Basile, Matilda Delgado, Jacques Distler, Dan Freed, Jonathan J. Heckman, Justin Kaidi, Jacob McNamara, Yuji Tachikawa, and Roberto Telléz Domínguez; thank you to all! Part of this project was completed while AD visited the Perimeter Institute for Theoretical Physics; research at Perimeter is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation.

Funders
Yuji Tachikawa
Canada Excellence Research Chairs, Government of Canada
Industry Canada
Ontario Ministry of Research, Innovation and Science

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1090/conm/802/16079

Cite this

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title = "Bordism for the 2-group symmetries of the heterotic and CHL strings",

abstract = "In the presence of a nonzero B-field, the symmetries of the E8{\texttimes}E8 heterotic string form a 2-group, or a categorified group, as do the symmetries of the CHL string. We express the bordism groups of the corresponding tangential structures as twisted string bordism groups, then compute them through dimension 11 modulo a few unresolved ambiguities. Then, we use these bordism groups to study anomalies and defects for these two string theories.",

author = "Arun Debray",

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year = "2024",

doi = "10.1090/conm/802/16079",

language = "English",

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Debray, A 2024, Bordism for the 2-group symmetries of the heterotic and CHL strings. in RM Kaufmann, M Markl & AA Voronov (eds), Higher Structures in Topology, Geometry, and Physics - AMS Special Session Higher Structures in Topology, Geometry, and Physics, 2022. Contemporary Mathematics, vol. 802, pp. 227-297, AMS Special Session on Higher Structures in Topology, Geometry, and Physics, 2022, Virtual, Online, 3/26/22. https://doi.org/10.1090/conm/802/16079

Bordism for the 2-group symmetries of the heterotic and CHL strings. / Debray, Arun.
Higher Structures in Topology, Geometry, and Physics - AMS Special Session Higher Structures in Topology, Geometry, and Physics, 2022. ed. / Ralph M. Kaufmann; Martin Markl; Alexander A. Voronov. 2024. p. 227-297 (Contemporary Mathematics; Vol. 802).

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

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Bordism for the 2-group symmetries of the heterotic and CHL strings

Abstract

Publication series

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Bibliographical note

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ASJC Scopus subject areas

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