M-theory, exceptional generalised geometry and superpotentials

Abstract

We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in eleven-dimensional supergravity. On a d-dimensional background, as first described by Hull, the action of the generalised geometrical O(d,d) symmetry group is replaced in EGG by the exceptional U-duality group E_d(d). The metric and form-field degrees of freedom combine into a single geometrical object, so that EGG naturally describes generic backgrounds with flux, and there is an EGG analogue of the Courant bracket which encodes the differential geometry. Our focus is on the case of seven-dimensional backgrounds with N=1 four-dimensional supersymmetry. The corresponding EGG is the generalisation of a G_2-structure manifold. We show it is characterised by an element ϕin a particular orbit of the 912 representation of E_7(7), which defines an SU(7) (subset of E_7(7)) structure. As an application, we derive the generic form of the four-dimensional effective superpotential, and show that it can be written in a universal form, as a homogeneous E_7(7)-invariant functional of ϕ.

36 pages, 3 tables, youngtab.sty for Young tableaux, typeset in JHEP style (HYPER VERSION); v2: references added (with corresponding comments)

References in corpus (17)

• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• A scan for new N=1 vacua on twisted tori
• SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
• Generalized N=1 Orientifold Compactifications and the Hitchin functionals
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Generalized Flux Vacua
• Supersymmetric sources, integrability and generalized-structure compactifications
• Warped Supersymmetry Breaking
• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Reformulating Supersymmetry with a Generalized Dolbeault Operator
• Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
• Topological sigma-models with H-flux and twisted generalized complex manifolds
• T-duality with H-flux: non-commutativity, T-folds and G x G structure
• Generalized Kaehler Potentials from Supergravity
• Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
• G2 Hitchin functionals at one loop

Cited by in corpus (168)

• Background independent action for double field theory
• Generalized Geometry and M theory
• Supergravity as Generalised Geometry I: Type II Theories
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• The gauge structure of generalised diffeomorphisms
• Exploring Double Field Theory
• A ten-dimensional action for non-geometric fluxes
• Duality Invariant Actions and Generalised Geometry
• SO(5,5) duality in M-theory and generalized geometry
• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• The local symmetries of M-theory and their formulation in generalised geometry
• Extended geometry and gauged maximal supergravity
• Lectures on Generalized Complex Geometry for Physicists
• Gauged Supergravities
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Covariant action for a string in doubled yet gauged spacetime
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Generalised geometry for string corrections
• M-theory and Type IIB from a Duality Manifest Action
• Comments on double field theory and diffeomorphisms
• Torsion-free generalized connections and Heterotic Supergravity
• Branes are Waves and Monopoles
• Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications
• Duality Invariance: From M-theory to Double Field Theory
• Global aspects of double geometry
• The Odd story of ${\alpha }^{\prime }$-corrections
• Leibniz algebroids, twistings and exceptional generalized geometry
• Boundary Terms in Generalized Geometry and doubled field theory
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• U-geometry : SL(5)
• Exceptional generalised geometry for massive IIA and consistent reductions
• U-dual fluxes and Generalized Geometry
• Duality Symmetric String and M-Theory
• Effective actions of non-geometric fivebranes
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Generalized gravity from modified DFT
• Systematics of consistent truncations from generalised geometry
• Strings and Branes are Waves
• E7(7) formulation of N=2 backgrounds
• The Geometry, Branes and Applications of Exceptional Field Theory
• Tri-Sasakian consistent reduction
• Poisson-Lie U-duality in Exceptional Field Theory
• Loops in exceptional field theory
• U-duality covariant gravity
• Supergravity as Generalised Geometry II: $E_{d(d)}\times {\mathbb{R}}^{+}$ and M theory
• Generalised diffeomorphisms for E${}_9$
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Generalised geometry from the ground up
• Extended geometries
• E${}_9$ exceptional field theory I. The potential
• T-duality and non-geometric solutions from double geometry
• Flux backgrounds from Twists
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets
• Exceptional Flux Compactifications
• Exactly marginal deformations from exceptional generalised geometry
• Dimensional Oxidation of Non-geometric Fluxes in Type II Orientifolds
• N=1 vacua in Exceptional Generalized Geometry
• SL(5) duality from canonical M2-brane
• On supersymmetric E11 exceptional field theory
• E${}_9$ exceptional field theory II. The complete dynamics
• E${}_{6(6)}$ Exceptional Field Theory: Review and Embedding of Type IIB
• Canonical approach to Courant brackets for D-branes
• Exceptional Calabi--Yau spaces: the geometry of $\mathcal{N}=2$ backgrounds with flux
• M5 algebra and SO(5,5) duality
• The exceptional generalised geometry of supersymmetric AdS flux backgrounds
• Type IIB flux vacua from G-theory II
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Seeking the balance: Patching double and exceptional field theories
• Hidden Gauge Structure of Supersymmetric Free Differential Algebras
• Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy
• E8 duality and dual gravity
• Double supergeometry
• Timelike U-dualities in Generalised Geometry
• Flux compactifications, twisted tori and doubled geometry
• Membrane Duality Revisited
• Type IIB flux vacua from G-theory I
• Generalised Space-time and Gauge Transformations
• Exceptional geometry and Borcherds superalgebras
• $\mathcal{N}=2$ consistent truncations from wrapped M5-branes
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• The free energy of N=2 supersymmetric AdS_4 solutions of M-theory
• Heterotic backgrounds via generalised geometry: moment maps and moduli
• On the exceptional generalised Lie derivative for $d\ge 7$
• Kaluza-Klein fermion mass matrices from Exceptional Field Theory and $\mathcal{N}=1$ spectra
• Introductory Lectures on Extended Supergravities and Gaugings
• Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Cosmological Implications from O(D,D)
• Generalised Structures for $\mathcal{N}=1$ AdS Backgrounds
• Einstein-Cartan Calculus for Exceptional Geometry
• Type II compactifications on manifolds with SU(2) x SU(2) structure
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• A note on large gauge transformations in double field theory
• Spin(7)-manifolds in compactifications to four dimensions
• Cancellation of divergences up to three loops in exceptional field theory
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Lobotomy of Flux Compactifications
• N=2 vacua in Generalized Geometry
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Democratic actions for type II supergravities
• Supersymmetric spectroscopy on AdS${}_4\times S^7$ and AdS${}_4\times S^6$
• U-gravity : $\mathbf{SL}(N)$
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Generalising G${}_{\text{2}}$ geometry: involutivity, moment maps and moduli
• Super-Chern-Simons spectra from Exceptional Field Theory
• New gaugings and non-geometry
• Thirty years of Erice on the brane
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• On symmetries and dynamics of exotic supermultiplets
• Exceptional algebroids and type IIB superstrings
• All maximal gauged supergravities with uplift
• Global Double Field Theory is Higher Kaluza-Klein Theory
• Currents, charges and algebras in exceptional generalised geometry
• Discreteness of time in the evolution of the universe
• Finite Transformations in Doubled and Exceptional Space
• Generalized geometric vacua with eight supercharges
• Gauge Transformation of Double Field Theory for Open String
• Generalized N=1 and N=2 structures in M-theory and type II orientifolds
• U-duality in three and four dimensions
• Teleparallelism in the algebraic approach to extended geometry
• Fermionic T-duality and U-duality in type II supergravity
• On the spin geometry of supergravity and string theory
• Supersymmetric AdS backgrounds and weak generalised holonomy
• Dimensional Reduction of the Generalized DBI
• Quantum Corrections in String Compactifications on SU(3) Structure Geometries
• Twistors and supertwistors for exceptional field theory
• Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory
• Supergravity without gravity and its BV formulation
• Extended geometry of magical supergravities
• Finite Gauge Transformations and Geometry in Extended Field Theory
• Perturbative F-theory 10-brane and M-theory 5-brane
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• The teleparallel complex
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Generalised Calibrations in AdS backgrounds from Exceptional Sasaki-Einstein Structures
• Strings, Branes and the Self-dual Solutions of Exceptional Field Theory
• Generalized geometry lectures on type II backgrounds
• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• Classical worldvolumes as generalised geodesics
• Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence
• On special geometry of the moduli space of string vacua with fluxes
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• $L_{\infty }$ algebras for extended geometry
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• C-spaces, generalized geometry and double field theory
• Heterotic type IIA duality with fluxes - towards the complete story
• Supergravity Fluxes and Generalised Geometry
• Brane current algebras and generalised geometry from QP manifolds
• Schwarzschild-AdS Black Holes in N=2 Geometric Flux Compactification
• Generalised Geometry and Flux Vacua
• Generalized Geometry and Partial Supersymmetry Breaking
• Torus Bundles, Automorphisms and T-Duality
• The landscape of G-structures in eight-manifold compactifications of M-theory
• Generalized geometry applied to 4d-supergravity
• Self-dual generalized metrics for pure $\mathcal{N}=1$ six-dimensional Supergravity
• Generalized Higher Gauge Theory and M5-brane dynamics. Proceedings: Higher structures in String and M-theory, Tohoku Forum for Creativity, March 7-11 2016
• Exactly Marginal Deformations and their Supergravity Duals
• T-duality and exceptional generalized geometry through symmetries of dg-manifolds
• Algebraic structures in exceptional geometry
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
• M-theory moduli spaces and torsion-free structures
• Exceptional algebroids and type IIA superstrings
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
• Extended Field Theories as higher Kaluza-Klein theories