Algebraic & Geometric Topology

Gravitational anomaly cancellation and modular invariance

Fei Han and Kefeng Liu

Full-text: Open access

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.

Article information

Source
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 91-113.

Dates
Received: 14 May 2013
Revised: 6 June 2013
Accepted: 18 June 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715795

Digital Object Identifier
doi:10.2140/agt.2014.14.91

Mathematical Reviews number (MathSciNet)
MR3158754

Zentralblatt MATH identifier
1291.53061

Subjects
Primary: 53C27: Spin and Spin$^c$ geometry 53C80: Applications to physics

Keywords
gravitational anomaly cancellation modular invariance

Citation

Han, Fei; Liu, Kefeng. Gravitational anomaly cancellation and modular invariance. Algebr. Geom. Topol. 14 (2014), no. 1, 91--113. doi:10.2140/agt.2014.14.91. https://projecteuclid.org/euclid.agt/1513715795


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