The Symmetry of M-Theories

Abstract

We consider the Cartan subalgebra of any very extended algebra G+++ where G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra, we find that for all very extensions G+++ of simple Lie algebras there are theories of gravity and matter, which admit classical solutions carrying representations of the Weyl group of G+++. We also identify the T and S-dualities of superstrings and of the bosonic string with Weyl reflections and outer automorphisms of well-chosen very extended algebras and we exhibit specific features of the very extensions. We take these results as indication that very extended algebras underlie symmetries of any consistent theory of gravity and matter, and might encode basic information for the construction of such theory.

Latex 41 pages, 2 figures. Introduction modified (and references renumbered) for better focusing. Minor changes in the bulk. Two references added

References in corpus (5)

• E10 and a "small tension expansion" of M Theory
• Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity
• Einstein billiards and overextensions of finite-dimensional simple Lie algebras
• The bosonic mother of fermionic D-branes
• Kac-Moody algebras in perturbative string theory

Cited by in corpus (77)

• Setting the boundary free in AdS/CFT
• The gauge structure of generalised diffeomorphisms
• The E_{11} origin of all maximal supergravities
• Very-extended Kac-Moody algebras and their interpretation at low levels
• Duality in linearized gravity
• Spacelike Singularities and Hidden Symmetries of Gravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
• Representations of G+++ and the role of space-time
• E_{11} origin of Brane charges and U-duality multiplets
• Branes are Waves and Monopoles
• Global aspects of double geometry
• E10 and SO(9,9) invariant supergravity
• Extended E8 Invariance of 11-Dimensional Supergravity
• Black holes in N=8 supergravity from SO(4,4) hidden symmetries
• E(11)-extended spacetime and gauged supergravities
• Dual fields and E_{11}
• Strings and Branes are Waves
• G+++ Invariant Formulation of Gravity and M-Theories: Exact Intersecting Brane Solutions
• An E9 multiplet of BPS states
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• On the underlying gauge group structure of D=11 supergravity
• Charge multiplets and masses for E(11)
• Hyperbolic billiards of pure D=4 supergravities
• Hidden Symmetries and Dirac Fermions
• Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
• Gradient Representations and Affine Structures in AE(n)
• Supersymmetric Domain Walls
• Off-Shell Hodge Dualities in Linearised Gravity and E11
• Hyperbolic Kac Moody Algebras and Einstein Billiards
• Seeking the balance: Patching double and exceptional field theories
• Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
• Aspects of higher curvature terms and U-duality
• On the E10/Massive Type IIA Supergravity Correspondence
• Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• G+++ and Brane Solutions
• Cosmological billiards and oxidation
• A Note on E11 and Three-dimensional Gauged Supergravity
• Intersection rules, dynamics and symmetries
• E_{11} and Higher Spin Theories
• Duality Symmetries and G^{+++} Theories
• E11 as E10 representation at low levels
• Generalised vielbeins and non-linear realisations
• Dualities and signatures of G++ invariant theories
• E11 and exceptional field theory
• The many vacua of gauged extended supergravities
• M-branes on U-folds
• Aspects of M-5 brane world volume dynamics
• An M-theory solution from null roots in E11
• Poincare Duality and G+++ algebra's
• Tachyon Kinks in Boundary String Field Theory
• Kac-Moody Algebras in M-theory
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• Superbranes, D=11 CJS supergravity and enlarged superspace coordinates/fields correspondence
• Orbits in Non-Supersymmetric Magic Theories
• Non-Supersymmetric Magic Theories and Ehlers Truncations
• Higher spin fields from indefinite Kac-Moody algebras
• Standard and Non-standard Extensions of Lie algebras
• On Brane Solutions Related to Non-Singular Kac-Moody Algebras
• Some simple predictions from E_{11} symmetry
• Infinite-Dimensional Gauge Structure of d=2 N=16 Supergravity
• M-Theory Solutions in Multiple Signatures from E_11
• A deformation of the Curtright action
• Gravitational Coset Models
• The emergence of fermions and the E11 content
• Connections between Kac-Moody algebras and M-theory
• N-Extended Lorentzian Kac-Moody algebras
• Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity
• Duality Covariant Solutions in Extended Field Theories
• Massive Type IIA Supergravity and E10
• Algebraic structures in M-theory
• Gravitational Billiards, Dualities and Hidden Symmetries
• From brane dynamics to a Kac-Moody invariant formulation of M-theories
• Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity
• Toda field theories and Calogero models associated to infinite Weyl groups
• Gravitational theories coupled to matter as invariant theories under Kac-Moody algebras