Perturbative Anomaly Inflow on Orbifolds

Hao Y. Zhang

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arXiv · 2608.23326

Perturbative Anomaly Inflow on Orbifolds

Hao Y. Zhang

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Abstract

We study perturbative anomaly inflow for effective theories supported on orbifold fixed loci of the internal geometry. Donnelly's equivariant APS theorem gives a fixed-point density, whose degree-$(d+2)$ component is identified as the anomaly polynomial of the $d$-dimensional effective theory. We apply the construction to six-dimensional A-type orbi-instanton theories engineered by $N$ M5-branes probing a transverse $\mathbb{C}^2/\mathbb{Z}_k$ singularity at an end-of-the-world M9-brane. For a flat $E_8$ connection specified by $\rho:\mathbb{Z}_k\to E_8$, we compute the non-identity ALE fixed-point class on the M9 wall. Its degree-eight component agrees with the complete Kac-label-dependent remainder conjectured in \cite{MOTZ} by Mekareeya-Ohmori-Tachikawa-Zafrir, including the $SU(2)_R$ and tangent-bundle curvatures. Together with the known M5/Ho\v{r}ava--Witten and ALE/Ho\v{r}ava--Witten terms, this reproduces the unflavored tensor-branch anomaly polynomial. This local equality further suggests a complete M-theory corner-inflow interpretation. The same prescription also be extended to include flavor symmetries as the centralizer of $E_8$.

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Hao Y. Zhang. 2026-08-24. Perturbative Anomaly Inflow on Orbifolds. https://arxiv.org/abs/2608.23326

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