Volume 14, issue 1 (2014)

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Gravitational anomaly cancellation and modular invariance

Fei Han and Kefeng Liu

Algebraic & Geometric Topology 14 (2014) 91–113
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-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.

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