Perturbative Anomaly Inflow on Orbifolds

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 (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}, 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).