M-theory, the signature theorem, and geometric invariants
arXiv:1012.1300 · doi:10.1103/PhysRevD.83.126010
Abstract
The equations of motion and the Bianchi identity of the C-field in M-theory are encoded in terms of the signature operator. We then reformulate the topological part of the action in M-theory using the signature, which leads to connections to the geometry of the underlying manifold, including positive scalar curvature. This results in a variation on the miraculous cancellation formula of Alvarez-Gaumé and Witten in twelve dimensions and leads naturally to the Kreck-Stolz s-invariant in eleven dimensions. Hence M-theory detects diffeomorphism type of eleven-dimensional (and seven-dimensional) manifolds, and in the restriction to parallelizable manifolds classifies topological eleven-spheres. Furthermore, requiring the phase of the partition function to be anomaly-free imposes restrictions on allowed values of the s-invariant. Relating to string theory in ten dimensions amounts to viewing the bounding theory as a disk bundle, for which we study the corresponding phase in this formulation.
arXiv comment17 pages
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Cited by in corpus (8)
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- Framed M-branes, corners, and topological invariants
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- M-Theory with Framed Corners and Tertiary Index Invariants
- Ninebrane structures
- Topological aspects of the NS5-brane
- On global anomalies in type IIB string theory
- Chern-Simons couplings, modular duality, and anomaly cancellation in abelian F-theory