Duality and cohomology in M-theory with boundary

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

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