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The algebra of anomaly interplay
by Joe Davighi, Nakarin Lohitsiri
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Joe Davighi · Nakarin Lohitsiri |
| Submission information | |
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| Preprint 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 |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| 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.
Author comments upon resubmission
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.
Published as SciPost Phys. 10, 074 (2021)