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arXiv · 2403.03953

Backfiring Bosonisation

Philip Boyle Smith·Yunqin Zheng
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Abstract

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.

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Philip Boyle Smith, Yunqin Zheng. 2024-03-06. Backfiring Bosonisation. https://arxiv.org/abs/2403.03953

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