Higher form symmetries and M-theory

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

Abstract

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.

Citation

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. https://doi.org/10.1007/jhep12%282020%29203

• 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
• DOI: https://doi.org/10.1007/jhep12%282020%29203
• Related Public URLs: https://arxiv.org/abs/2005.12831