Generalised Geometry for M-Theory

Abstract

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge field on which there is a natural action of the group $E_d$. This provides a framework for the discussion of M-theory solutions with flux. A different generalisation is to d-dimensional manifolds with a metric, 2-form gauge field and a set of p-forms for $p$ either odd or even on which there is a natural action of the group $E_{d+1}$. This is useful for type IIA or IIB string solutions with flux. Further generalisations give extended tangent bundles and extended spin bundles relevant for non-geometric backgrounds. Special structures that arise for supersymmetric backgrounds are discussed.

31 pages

References in corpus (3)

• Holonomy and Symmetry in M-theory
• Generalized Hyperkaehler Geometry and Supersymmetry
• Generalized complex geometry and supersymmetric non-linear sigma models

Cited by in corpus (9)

• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Axionic symmetry gaugings in N=4 supergravities and their higher-dimensional origin
• D-branes and doubled geometry
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• Flux compactifications, twisted tori and doubled geometry
• Type II compactifications on manifolds with SU(2) x SU(2) structure
• M-branes on U-folds
• Ramond-Ramond Fields, Cohomology and Non-Geometric Fluxes
• Non-unimodular reductions and N = 4 gauged supergravities