Gravitational anomaly cancellation and modular invariance

In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $(4 k + 2)$ –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 $4 k + 1$ , we derive anomaly cancellation formulas for index gerbes. In dimension $4 k + 3$ , we obtain certain results about eta invariants, which are interesting in spectral geometry.

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Keywords

gravitational anomaly cancellation, modular invariance

Mathematical Subject Classification 2010

Primary: 53C27, 53C80

References

Publication

Received: 14 May 2013

Revised: 6 June 2013

Accepted: 18 June 2013

Preview posted: 21 November 2013

Published: 9 January 2014

Authors

Fei Han
Department of Mathematics National University of Singapore Block S17, 10 Lower Kent Ridge Road Singapore 119076 Singapore

Kefeng Liu
Department of Mathematics University of California, Los Angeles 405 Hilgard Avenue Los Angeles, CA 90095 USA
http://www.math.ucla.edu/~liu

Volume 14, issue 1 (2014)

Fei Han and Kefeng Liu

Abstract