Elliptic genus, anomaly cancellation and heterotic M-theory

We derive global consistency condition for strongly coupled heterotic string in the presence of M5-branes. Its elliptic genus is interpretable as generating functional anomaly polynomials and so, on anomaly-free vacua, both holomorphic modular invariant. In basis, we identify properties by calculating phase. By interpreting refinement parameters background curvature tangent vector bundles, show that extended Bianchi identity Kalb--Ramond field M-theory satisfied arbitrary numbers