Gravitational Anomaly Cancellation and Modular Invariance

2010/07/29 by Fei Han, Kefeng Liu, Han, Fei +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.1007.5295

arxiv created 2010/07/29 · openalex publication_date 2010/07/29 · arxiv updated 2010/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (\citeAW) 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.

Citations

• The index of the dirac operator in loop space

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