Elliptic Genus, Anomaly Cancellation and Heterotic M-theory

TL;DR

This paper derives consistency conditions for heterotic M-theory with M5-branes, linking elliptic genus properties to anomaly cancellation, modular invariance, and Bianchi identities, advancing understanding of anomaly-free vacua in string theory.

Contribution

It introduces a novel interpretation of the elliptic genus as an anomaly polynomial generator and establishes extended Bianchi identities in heterotic M-theory with multiple M5-branes.

Findings

Elliptic genus is holomorphic and modular invariant on anomaly-free vacua.

Identifies modular properties through phase calculations in a holomorphic basis.

Derives extended Bianchi identity incorporating M5-branes and background curvatures.

Abstract

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