Global Anomalies in Sigma Models with Majorana--Weyl Fermions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915453121593344 |
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| author | Choi, Changha |
| author_facet | Choi, Changha |
| contents | We investigate a global sigma model anomaly in two-dimensional sigma models with Majorana--Weyl fermions coupled to a sigma model field with target space~$G$. The anomaly originates from the nontrivial topology of the space of maps and manifests as a phase in the fermion path integral. Using the global anomaly formula expressed in terms of the reduced~$η$-invariant, we demonstrate that this anomaly modifies the standard quantization condition of the Wess--Zumino term on~$G$, in close analogy with the three-dimensional parity anomaly. However, our situation is more refined and highlights a qualitatively new phenomenon in two dimensions: whereas in three dimensions the anomalous quantization restricts the level to lie in a half-integer lattice, here it can force the level to take \emph{arbitrary real values}. Furthermore, our results support the consistency of the low-energy description proposed by Gaiotto, Johnson-Freyd, and Witten for three-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory on an interval, by highlighting a subtle and qualitatively distinct nature of the sigma-model anomalies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Anomalies in Sigma Models with Majorana--Weyl Fermions Choi, Changha High Energy Physics - Theory We investigate a global sigma model anomaly in two-dimensional sigma models with Majorana--Weyl fermions coupled to a sigma model field with target space~$G$. The anomaly originates from the nontrivial topology of the space of maps and manifests as a phase in the fermion path integral. Using the global anomaly formula expressed in terms of the reduced~$η$-invariant, we demonstrate that this anomaly modifies the standard quantization condition of the Wess--Zumino term on~$G$, in close analogy with the three-dimensional parity anomaly. However, our situation is more refined and highlights a qualitatively new phenomenon in two dimensions: whereas in three dimensions the anomalous quantization restricts the level to lie in a half-integer lattice, here it can force the level to take \emph{arbitrary real values}. Furthermore, our results support the consistency of the low-energy description proposed by Gaiotto, Johnson-Freyd, and Witten for three-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory on an interval, by highlighting a subtle and qualitatively distinct nature of the sigma-model anomalies. |
| title | Global Anomalies in Sigma Models with Majorana--Weyl Fermions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.14895 |