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Higher form symmetries and M-theory

Albertini, Federica; Del Zotto, Michele; García Etxebarria, Iñaki; Hosseini, Saghar S.

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Michele Del Zotto

Saghar S. Hosseini


We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) ’t Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d N = 1 SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d N = 1 SYM theory, where we recover it from a mixed ’t Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed ’t Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities.


Albertini, F., Del Zotto, M., García Etxebarria, I., & Hosseini, S. S. (2020). Higher form symmetries and M-theory. Journal of High Energy Physics, 2020(12), Article 203.

Journal Article Type Article
Acceptance Date Nov 19, 2020
Online Publication Date Dec 30, 2020
Publication Date 2020-12
Deposit Date Jan 4, 2021
Publicly Available Date Apr 13, 2021
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2020
Issue 12
Article Number 203
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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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