Elliptic genera and E8 Bundles in odd dimensions

TL;DR

This paper develops new anomaly cancellation formulas in odd dimensions by integrating modular forms with E8 and E8*E8 bundles on spin manifolds, expanding the mathematical framework for anomaly analysis.

Contribution

It introduces a systematic method to twist and generalize modular forms associated with E8 bundles, deriving novel anomaly cancellation formulas in odd-dimensional settings.

Findings

New series of anomaly cancellation formulas derived

Modular forms associated with E8 bundles generalized

Framework applicable to odd-dimensional spin manifolds

Abstract

This paper aims to derive new anomaly cancellation formulas by combining modular forms with E8 and E8*E8 bundles. To this end, we systematically twist and generalize known SL(2,Z) modular forms to define new modular forms associated with these bundles on odd-dimensional spin and spin^c manifolds, leading to a new series of anomaly cancellation formulas.