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

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• Nongeometric Flux Compactifications
• New Supersymmetric String Compactifications
• Doubled Geometry and T-Folds
• Generalized structures of N=1 vacua
• Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds
• Duality Twists, Orbifolds, and Fluxes
• Mirror Symmetry in Generalized Calabi-Yau Compactifications
• Geometric Constructions of Nongeometric String Theories
• Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities
• Generalised T-Duality and Non-Geometric Backgrounds
• Instantons, Poisson structures and generalized Kaehler geometry
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Constructing Nongeometric Vacua in String Theory
• Strongly Coupled Gravity and Duality
• Gravitational Duality, Branes and Charges
• Hidden Spacetime Symmetries and Generalized Holonomy in M-theory
• Generalised $G_2$-structures and type IIB superstrings
• Generalized complex manifolds and supersymmetry
• Generalized Kahler manifolds and off-shell supersymmetry
• Flux Compactifications of M-Theory on Twisted Tori
• Holonomy and Symmetry in M-theory
• D-branes in Nongeometric Backgrounds
• A Note on Compactifications on Spin(7)-Holonomy Manifolds
• Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models
• Generalized complex geometry, generalized branes and the Hitchin sigma model
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• Worldsheet CFTs for Flat Monodrofolds
• Generalized Kahler Geometry from supersymmetric sigma models
• Quantum Mechanics of the Doubled Torus
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• BPS Supermultiplets in Five Dimensions
• The topology of U-duality (sub-)groups
• Generalized Hyperkaehler Geometry and Supersymmetry
• Modified pure spinors and mirror symmetry
• On T-folds, G-structures and Supersymmetry
• Generalized complex geometry and supersymmetric non-linear sigma models
• Tachyon condensation and D-branes in generalized geometries
• Generalised HyperKaehler Manifolds in String Theory
• U-duality (sub-)groups and their topology

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• Extended Riemannian Geometry I: Local Double Field Theory
• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• Canonical approach to Courant brackets for D-branes
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• Introductory Lectures on Extended Supergravities and Gaugings
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5
• The Pontryagin Class for Pre-Courant Algebroids
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• Perturbative F-theory 10-brane and M-theory 5-brane
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• Generalised Calibrations in AdS backgrounds from Exceptional Sasaki-Einstein Structures
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• Exceptional Field Theory for $E_{6(6)}$ supergravity
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• Duality Covariant Solutions in Extended Field Theories
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• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• Algebraic structures in exceptional geometry
• Exceptional algebroids and type IIA superstrings
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• Extended Field Theories as higher Kaluza-Klein theories
• Exactly Marginal Deformations and their Supergravity Duals
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• Generalized Higher Gauge Theory and M5-brane dynamics. Proceedings: Higher structures in String and M-theory, Tohoku Forum for Creativity, March 7-11 2016
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
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