Gravitational Anomaly Cancellation and Modular Invariance

TL;DR

This paper develops general formulas for gravitational anomaly cancellation across various dimensions using modular and characteristic forms, extending known results and exploring spectral geometry implications.

Contribution

It introduces unified anomaly cancellation formulas applicable in multiple dimensions, including new results for index gerbes and eta invariants.

Findings

Unified anomaly cancellation formulas for all dimensions.

Extension of Alvarez-Gaumé and Witten formulas to higher dimensions.

New insights into eta invariants in spectral geometry.

Abstract

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.