Gravitational anomaly cancellation and modular invariance

Abstract

In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $\left(4k+2\right)$–dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaumé and Witten in dimensions $2$, $6$ and $10$ [Nuclear Phys. B 234(2) (1984) 269–330] as special cases. In dimension $4k+1$, we derive anomaly cancellation formulas for index gerbes. In dimension $4k+3$, we obtain certain results about eta invariants, which are interesting in spectral geometry.