Anomaly Cancellation and Modularity. II: $E_8\times E_8$ case

TL;DR

This paper demonstrates that anomaly factorization formulas for the gauge groups E8×E8 and E8 can be derived from modular forms of weight 14, providing new generalizations and a Hořava-Witten type formula.

Contribution

It shows the derivation of anomaly factorization formulas from modular forms and introduces generalizations and a new Hořava-Witten type formula.

Findings

Anomaly formulas for E8×E8 and E8 derived from modular forms.

Established generalizations of these formulas.

Obtained a new Hořava-Witten type factorization formula.

Abstract

In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group $E_8\times E_8$ and the Ho\v{r}ava-Witten anomaly factorization formula for the gauge group $E_8$ can be derived through modular forms of weight 14. This answers a question of J. H. Schwarz. We also establish generalizations of these factorization formulas and obtain a new Ho\v{r}ava-Witten type factorization formula.