Cubic forms, anomaly cancellation and modularity

Fei Han National University of Singapore Ruizhi Huang Chinese Academy of Sciences Kefeng Liu University of California at Los Angeles, Weiping Zhang Nankai University

Differential Geometry Geometric Analysis and Geometric Topology Mathematical Physics Algebraic Topology and General Topology mathscidoc:2110.10001

46, 2021.10
Recently Freed and Hopkins [11] proved that there is no parity anomaly in M-theory on pin+ manifolds in the low-energy field theory approximation, and they also developed an algebraic theory of cubic forms. Earlier Witten [33] proved the anomaly cancellation for spin manifolds by introducing the E8-bundle technique. Motivated by the cubic forms and the anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spinc, spinω2 and orientable 12- manifolds respectively. We relate them to η-invariants when the manifolds are with boundary, and mod 2 indices on 10 dimensional characteristic submanifolds when the manifolds are spinc or spinω2 . Our method of producing these cubic forms is a combination of (generalized) Witten classes and the character of the basic representation of affine E8.
Anomaly cancellation, M-theory, Cubic form, Modular form, Twisted Witten class, Spin and spinc classes
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  title={Cubic forms, anomaly cancellation and modularity},
  author={Fei Han, Ruizhi Huang, Kefeng Liu, and Weiping Zhang},
Fei Han, Ruizhi Huang, Kefeng Liu, and Weiping Zhang. Cubic forms, anomaly cancellation and modularity. 2021. pp.46.
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