Gravitational Anomaly Cancellation and Modular Invariance

Details Gravitational Anomaly Cancellation and Modular Invariance Gravitational Anomaly Cancellation and Modular Invariance

2010-07-29

arxiv.org/abs/1007.5295v1

Physics

Mathematical Physics

Scientific paper

In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $4k+2$ dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaum\'e and Witten in dimensions 2, 6 and 10 (\cite{AW}) 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.

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