M-theory, the signature theorem, and geometric invariants

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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 12 dimensions and leads naturally to the Kreck-Stolz s-invariant in 11 dimensions. Hence M-theory detects the diffeomorphism type of 11-dimensional (and seven-dimensional) manifolds and in the restriction to parallelizable manifolds classifies topological 11 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.

Original languageEnglish (US)
Article number126010
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number12
StatePublished - Jun 22 2011

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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