Very-extended Kac-Moody algebras and their interpretation at low levels

Abstract

We analyse the very-extended Kac-Moody algebras as representations in terms of certain A_d subalgebras and find the generators at low levels. Our results for low levels agree precisely with the bosonic field content of the theories containing gravity, forms and scalars which upon reduction to three dimensions can be described by a non-linear realisation. We explain how the Dynkin diagrams of the very-extended algebras encode information about the field content and generalised T-duality transformations.

1+41 pages, 10 figures, LaTeX2e

References in corpus (27)

• E_11 and M Theory
• E10 and a "small tension expansion" of M Theory
• $E_{11}$, SL(32) and Central Charges
• Chaos in Superstring Cosmology
• E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology
• Hyperbolic Kac-Moody Algebras and Chaos in Kaluza-Klein Models
• Strongly Coupled Gravity and Duality
• Hidden Superconformal Symmetry in M Theory
• Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity
• Kac-Moody Symmetries of IIB Supergravity
• The Symmetry of M-Theories
• Higher-dimensional Origin of D=3 Coset Symmetries
• A class of Lorentzian Kac-Moody algebras
• Borcherds symmetries in M-theory
• The group theory of oxidation
• Finite in All Directions
• Coset Symmetries in Dimensionally Reduced Bosonic String Theory
• Massive IIA Supergravity as a Non-linear Realisation
• Consistent and covariant anomalies in six-dimensional supergravity
• Symmetries of the Bosonic String S-Matrix
• Physical States and String Symmetries
• Intersection rules, dynamics and symmetries
• E11 as E10 representation at low levels
• The bosonic mother of fermionic D-branes
• Brane fusion in the bosonic string and the emergence of fermionic strings
• The Spontaneous Compactification of the Closed Bosonic String
• Kac-Moody algebras in perturbative string theory

Cited by in corpus (101)

• The E_{11} origin of all maximal supergravities
• E(11) and the Embedding Tensor
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
• M-theory and Type IIB from a Duality Manifest Action
• IIB Supergravity Revisited
• Representations of G+++ and the role of space-time
• E_{11} origin of Brane charges and U-duality multiplets
• String Solitons and T-duality
• E_11: Sign of the times
• E10 and SO(9,9) invariant supergravity
• E(11)-extended spacetime and gauged supergravities
• Holography in asymptotically flat space-times and the BMS group
• Gauge Theories, Duality Relations and the Tensor Hierarchy
• Kac-Moody Spectrum of (Half-)Maximal Supergravities
• IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories
• Dual fields and E_{11}
• G+++ Invariant Formulation of Gravity and M-Theories: Exact Intersecting Brane Solutions
• Counting supersymmetric branes
• An E9 multiplet of BPS states
• D-Brane Wess-Zumino Terms and U-Duality
• Three-forms in Supergravity and Flux Compactifications
• Branes and wrapping rules
• Loops in exceptional field theory
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• IIB supergravity and E10
• Beyond E11
• Non-linear parent action and dual gravity
• IIA/IIB Supergravity and Ten-forms
• The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
• Brane orbits
• Gradient Representations and Affine Structures in AE(n)
• $P$ fluxes and exotic branes
• A master exceptional field theory
• Supersymmetric Domain Walls
• On supersymmetric E11 exceptional field theory
• Hyperbolic Kac Moody Algebras and Einstein Billiards
• RG Cascades in Hyperbolic Quiver Gauge Theories
• Weaving the Exotic Web
• E11 must be a symmetry of strings and branes
• A brief review of E theory
• IIA and IIB spinors from K(E10)
• Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
• Local E(11)
• On the E10/Massive Type IIA Supergravity Correspondence
• Exotic E11 branes as composite gravitational solutions
• E_{11}, ten forms and supergravity
• 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
• A Note on E11 and Three-dimensional Gauged Supergravity
• Duality Symmetries and G^{+++} Theories
• Kappa-symmetric SL(2,R) covariant D-brane actions
• E10 and Gauged Maximal Supergravity
• E11, Romans theory and higher level duality relations
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Dualities and signatures of G++ invariant theories
• Five-dimensional Supergravity and Hyperbolic Kac-Moody Algebra G2H
• On symmetries and dynamics of exotic supermultiplets
• Arithmetic and Hyperbolic Structures in String Theory
• $E_{11}$, Borcherds algebras and maximal supergravity
• Non-propagating degrees of freedom in supergravity and very extended G_2
• Pure type I supergravity and DE(10)
• Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
• Real forms of extended Kac-Moody symmetries and higher spin gauge theories
• Local E(11) and the gauging of the trombone symmetry
• Can dual gravity be reconciled with E11?
• Poincare Duality and G+++ algebra's
• Time-like T-duality algebra
• Oxidizing Borcherds symmetries
• Wrapping rules (in) string theory
• On the different formulations of the E11 equations of motion
• Some Algebraic Aspects of Half-BPS Bound States in M-Theory
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• Sugawara-type constraints in hyperbolic coset models
• E11 and Spheric Vacuum Solutions of Eleven- and Ten dimensional Supergravity Theories
• Kac-Moody Algebras in M-theory
• Killing Spinor Equations from Nonlinear Realisations
• Bound States of String Theory and Beyond
• Non-Supersymmetric Magic Theories and Ehlers Truncations
• Orbits in Non-Supersymmetric Magic Theories
• Hidden Borcherds symmetries in Z_n orbifolds of M-theory and magnetized D-branes in type 0' orientifolds
• Standard and Non-standard Extensions of Lie algebras
• Hidden Symmetry Unmasked: Matrix Theory and E(11)
• Higher spin fields from indefinite Kac-Moody algebras
• Type II Double Field Theory in Superspace
• A deformation of the Curtright action
• Space-filling branes & gaugings
• Gravitational Coset Models
• The very-extended trombone
• Connections between Kac-Moody algebras and M-theory
• The emergence of fermions and the E11 content
• Exotic branes and mixed-symmetry potentials I: predictions from $E_{11}$ symmetry
• Unifying R-symmetry in M-theory
• Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity
• Hidden Symmetries of M-Theory and Its Dynamical Realization
• Hyperbolic Invariance in Type II Superstrings
• Algebraic structures in M-theory
• Gravitational Billiards, Dualities and Hidden Symmetries
• Massive Type IIA Supergravity and E10
• The Two-Parameter Brane Sigma-Model and Extended Solutions of M-Theory