Duality and cohomology in M-theory with boundary

Hisham Sati

    Research output: Contribution to journalArticle

    Abstract

    We consider geometric and analytical aspects of M-theory on a manifold with boundary Y11. The partition function of the C-field requires summing over harmonic forms. When Y11 is closed, Hodge theory gives a unique harmonic form in each de Rham cohomology class, while in the presence of a boundary the Hodge-Morrey-Friedrichs decomposition should be used. This leads us to study the boundary conditions for the C-field. The dynamics and the presence of the dual to the C-field gives rise to a mixing of boundary conditions with one being Dirichlet and the other being Neumann. We describe the mixing between the corresponding absolute and relative cohomology classes via Poincaré duality angles, which we also illustrate for the M5-brane as a tubular neighborhood. Several global aspects are then considered. We provide a systematic study of the extension of the E8 bundle and characterize obstructions. Considering Y11 as a fiber bundle, we describe how the phase looks like on the base, hence providing dimensional reduction in the boundary case via the adiabatic limit of the eta invariant. The general use of the index theorem leads to a new effect given by a gravitational Chern-Simons term CS11 on Y11 whose restriction to the boundary would be a generalized WZW model. This suggests that holographic models of M-theory can be viewed as a sector within this index-theoretic approach.

    Original languageEnglish (US)
    Pages (from-to)1284-1297
    Number of pages14
    JournalJournal of Geometry and Physics
    Volume62
    Issue number5
    DOIs
    StatePublished - May 1 2012

    Fingerprint

    M-Theory
    homology
    Harmonic Forms
    Cohomology
    Duality
    Hodge Theory
    bundles
    Eta Invariant
    De Rham Cohomology
    Boundary conditions
    Index Theorem
    Dimensional Reduction
    Manifolds with Boundary
    Fiber Bundle
    boundary conditions
    Branes
    Obstruction
    harmonics
    Partition Function
    Dirichlet

    Keywords

    • Chern-Simons invariants
    • Dirichlet-to-Neumann map
    • Eta invariants
    • Gauge theory on manifold with boundary
    • Hodge theory
    • M-theory on manifold with boundary

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Geometry and Topology

    Cite this

    Duality and cohomology in M-theory with boundary. / Sati, Hisham.

    In: Journal of Geometry and Physics, Vol. 62, No. 5, 01.05.2012, p. 1284-1297.

    Research output: Contribution to journalArticle

    Sati, Hisham. / Duality and cohomology in M-theory with boundary. In: Journal of Geometry and Physics. 2012 ; Vol. 62, No. 5. pp. 1284-1297.
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