Backfiring Bosonisation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929266446303232 |
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| author | Smith, Philip Boyle Zheng, Yunqin |
| author_facet | Smith, Philip Boyle Zheng, Yunqin |
| contents | For a fermionic quantum field theory in $d=1+1$ dimensions, there is a subtle difference between summing over spin structures and gauging $(-1)^F$. If the gravitational anomaly vanishes mod 16, then both operations are equivalent and yield a bosonic theory. But if the gravitational anomaly only vanishes mod 8, then only gauging $(-1)^F$ is allowed, and the result is a fermionic theory. Our goal is to understand in detail how this happens, despite the fact $(-1)^F$ is defined in terms of shifting the spin structure, which would naïvely suggest that both operations are equivalent. We do this from three perspectives: an abstract view in terms of anomalies, explicit CFT calculations, and a Symmetry TFT perspective. To conclude, we illustrate our results using the heterotic string and the famous self-triality of 8 Majorana-Weyl fermions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_03953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Backfiring Bosonisation Smith, Philip Boyle Zheng, Yunqin High Energy Physics - Theory Strongly Correlated Electrons For a fermionic quantum field theory in $d=1+1$ dimensions, there is a subtle difference between summing over spin structures and gauging $(-1)^F$. If the gravitational anomaly vanishes mod 16, then both operations are equivalent and yield a bosonic theory. But if the gravitational anomaly only vanishes mod 8, then only gauging $(-1)^F$ is allowed, and the result is a fermionic theory. Our goal is to understand in detail how this happens, despite the fact $(-1)^F$ is defined in terms of shifting the spin structure, which would naïvely suggest that both operations are equivalent. We do this from three perspectives: an abstract view in terms of anomalies, explicit CFT calculations, and a Symmetry TFT perspective. To conclude, we illustrate our results using the heterotic string and the famous self-triality of 8 Majorana-Weyl fermions. |
| title | Backfiring Bosonisation |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.03953 |