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The algebra of anomaly interplay

by Joe Davighi, Nakarin Lohitsiri

Submission summary

As Contributors: Joe Davighi · Nakarin Lohitsiri
Arxiv Link: https://arxiv.org/abs/2011.10102v3 (pdf)
Date accepted: 2021-03-11
Date submitted: 2021-03-02 16:20
Submitted by: Lohitsiri, Nakarin
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.

Published as SciPost Phys. 10, 074 (2021)



Author comments upon resubmission

We thank the referees for their valuable suggestions. We have considered them and revised our manuscript accordingly. Changes specific to them are listed directly as responses to the referees' comments.

List of changes

1. Added a figure (Figure 1) depicting our extension of the $U(2)$ mapping torus to a 6-manifold it bounds.
2. Elaborated on the failure of surjectivity in the 2d example (end of section 4).
3. Added three unnumbered subsections inside sections 4 and 5.1 for readability.
4. Removed the numbering of the subsection 7.2.1.
5. Added an explicit specification in the titles of Appendices A.3 and A.4 and in the captions of tables 1 and 2 that the results are valid when m>1.
6. See the responses to the referees' comments for other changes.

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