AI 中文总结
该研究将Donnelly等变APS定理应用于六维A型轨形瞬子理论，计算M9壁的非恒等ALE不动点类，重现无味道张量分支反常多项式，为M理论角落流入提供解释并可扩展至含味道对称的情况。
AI 中文摘要
我们研究支撑在内部几何的轨形不动点轨迹上的有效理论的微扰反常流入。Donnelly的等变APS定理给出了不动点密度，其次数为(d+2)的分量被认定为d维有效理论的反常多项式。我们将该构造应用于六维A型轨形瞬子理论，该理论由N个M5膜探测横截的ℂ²/ℤₖ奇点并处于世界末端M9膜上构建。对于由ρ:ℤₖ→E₈指定的平坦E₀联络，我们计算了M9壁上的非恒等ALE不动点类，其八次分量与文献[MOTZ]中猜想的完全依赖于Kac标记的余项一致，包括SU(2)ᵣ和切丛曲率。结合已知的M5/Hořava–Witten项和ALE/Hořava–Witten项，这重现了无味道的张量分支反常多项式，该局部等式进一步暗示了完整的M理论角落流入解释。该方案也可扩展以包含作为E₈中心化子的味道对称性。
英文摘要
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 $ρ:\mathbb{Z}_k\to E_8$, 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/Hořava--Witten and ALE/Hořava--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 $E_8$.
Comments31 pages + an appendix, 1 figure; v2: minor syntax and reference update
