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Fermionic Higher-form Symmetries

by Yi-Nan Wang, Yi Zhang

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Submission summary

Authors (as registered SciPost users): Yinan Wang · Yi Zhang
Submission information
Preprint Link: scipost_202304_00003v3  (pdf)
Date accepted: 2023-08-29
Date submitted: 2023-08-14 16:39
Submitted by: Wang, Yinan
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


In this paper, we explore a new type of global symmetries-the fermionic higher-form symmetries. They are generated by topological operators with fermionic parameter, which act on fermionic extended objects. We present a set of field theory examples with fermionic higher-form symmetries, which are constructed from fermionic tensor fields. They include the free fermionic tensor theories, a new type of fermionic topological quantum field theories, as well as the exotic 6d (4,0) theory. We also discuss the gauging and breaking of such global symmetries and the relation to the no global symmetry swampland conjecture.

Author comments upon resubmission

Dear Editor,

According to Referee 2's comment, we have added a short Appendix B on the vacuum expectation value of the fermionic Wilson loops in the free field case. We have also responded to the referees' questions by comments on the SciPost webpage.

Best regards,
The authors

List of changes

We added a short Appendix B on the vacuum expectation value (VEV) of the fermionic Wilson loops. In particular, we gave an example of a free Rarita-Schwinger field in 4d, where we computed the VEV of the fermionic Wilson loop and confirmed that it obeys the perimeter law.

Published as SciPost Phys. 15, 142 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-8-26 (Invited Report)


The authors have satisfactorily clarified the question raised in my previous report.

I consider the latest version of the manuscript fit for publication in SciPost. The paper has the potential for being of great impact in the field of generalized symmetries, and meets the acceptance criteria.

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Anonymous Report 1 on 2023-8-22 (Invited Report)


I recommend the present version of the manuscript for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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