Global anomalies in sigma models with Majorana-Weyl fermions
- 1Perimeter Institute for Theoretical Physics
Abstract
A bstract : 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 holonomy 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 arbitrary real values . Furthermore, our results support the consistency of the low-energy description proposed by Gaiotto, Johnson-Freyd, and Witten for three-dimensional 𝒩 N = 1 supersymmetric Yang-Mills theory on an interval, by highlighting a subtle and qualitatively distinct nature of the sigma-model anomalies.
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BibTeX
@article{choi2026global,
title = {{Global anomalies in sigma models with Majorana-Weyl fermions}},
author = {Changha Choi},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)146},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)146},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Global anomalies in sigma models with Majorana-Weyl fermions
AU - Changha Choi
PY - 2026
DA - 2026/10/14
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)146
UR - https://link.springer.com/article/10.1007/JHEP10(2026)146
AB - A bstract : 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 holonomy 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 arbitrary real values . Furthermore, our results support the consistency of the low-energy description proposed by Gaiotto, Johnson-Freyd, and Witten for three-dimensional 𝒩 N = 1 supersymmetric Yang-Mills theory on an interval, by highlighting a subtle and qualitatively distinct nature of the sigma-model anomalies.
SN - 1029-8479
ER -