Modular Invariance and Anomaly Cancellation Formulas for Fiber Bundles

By combining modular invariance of characteristic forms and the family index theory, we obtain some new anomaly cancellation formulas for any dimension under the not top degree component. For a fiber bundle of dimension (4l−2), we obtain the anomaly cancellation formulas for the determinant line bundle. For the fiber bundle with a dimension of (4l−3), we derive the anomaly cancellation formulas of the index gerbes. For the fiber bundle of dimension (4l−1), we obtain some results of the eta invariants. Moreover, we give some anomaly cancellation formulas of the Chen–Connes character and the higher elliptic genera.