E8 bundles and some new anomaly cancellation formulas

Abstract

Using $E_8$ bundles, we construct some new modular forms over $SL(2,\mathbf{Z})$, $\hat{I}{“}^0(2)$ and $\hat{I}{“}_0(2)$ and get some new anomaly cancellation formulas of characteristic forms which generalize some anomaly cancellation formulas in [13].