M-theory, the signature theorem, and geometric invariants

Hisham Sati

    Research output: Contribution to journalArticle

    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 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
    Volume83
    Issue number12
    DOIs
    StatePublished - Jun 22 2011

    Fingerprint

    theorems
    signatures
    constrictions
    cancellation
    string theory
    bundles
    partitions
    equations of motion
    curvature
    anomalies
    scalars
    formulations
    operators
    geometry

    ASJC Scopus subject areas

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

    Cite this

    M-theory, the signature theorem, and geometric invariants. / Sati, Hisham.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 83, No. 12, 126010, 22.06.2011.

    Research output: Contribution to journalArticle

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