Anomaly Cancellation and Modularity. II: $E_8\times E_8$ case
  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. 
Fei Han, Kefeng Liu and Weiping Zhang
hep-th math-ph math.DG math.MP