G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions

Abstract

We present a tentative formulation of theories of gravity with suitable matter content, including in particular pure gravity in D dimensions, the bosonic effective actions of M-theory and of the bosonic string, in terms of actions invariant under very-extended Kac-Moody algebras G+++. We conjecture that they host additional degrees of freedom not contained in the conventional theories. The actions are constructed in a recursive way from a level expansion for all very-extended algebras G+++. They constitute non-linear realisations on cosets, a priori unrelated to space-time, obtained from a modified Chevalley involution. Exact solutions are found for all G+++. They describe the algebraic properties of BPS extremal branes, Kaluza-Klein waves and Kaluza-Klein monopoles. They illustrate the generalisation to all G+++ invariant theories of the well-known duality properties of string theories by expressing duality as Weyl invariance in G+++. Space-time is expected to be generated dynamically. In the level decomposition of E8+++ = E11, one may indeed select an A10 representation of generators Pa which appears to engender space-time translations by inducing infinite towers of fields interpretable as field derivatives in space and time.

arXiv commentLatex 45 pages, 1 figure. Discussion on pages 19 and 20 altered. Appendix B amplified. 4 footnotes added. 2 references added. Acknowledgments updated. Additional minor corrections

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Cited by in corpus (72)

• Duality in linearized gravity
• Spacelike Singularities and Hidden Symmetries of Gravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• Representations of G+++ and the role of space-time
• E_{11} origin of Brane charges and U-duality multiplets
• Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
• E_11: Sign of the times
• E10 and SO(9,9) invariant supergravity
• Extended E8 Invariance of 11-Dimensional Supergravity
• Higher order M theory corrections and the Kac-Moody algebra E10
• K(E10), Supergravity and Fermions
• The Geometry, Branes and Applications of Exceptional Field Theory
• G+++ Invariant Formulation of Gravity and M-Theories: Exact Intersecting Brane Solutions
• Counting supersymmetric branes
• An E9 multiplet of BPS states
• Branes and wrapping rules
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• IIB supergravity and E10
• Beyond E11
• Hidden Symmetries and Dirac Fermions
• Gradient Representations and Affine Structures in AE(n)
• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
• Supersymmetric Domain Walls
• A brief review of E theory
• Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
• IIA and IIB spinors from K(E10)
• E10 Cosmology
• On the E10/Massive Type IIA Supergravity Correspondence
• Exotic E11 branes as composite gravitational solutions
• K(E9) from K(E10)
• E_{11}, ten forms and supergravity
• Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• G+++ and Brane Solutions
• A Note on E11 and Three-dimensional Gauged Supergravity
• E10 and Gauged Maximal Supergravity
• Dualities and signatures of G++ invariant theories
• Five-dimensional Supergravity and Hyperbolic Kac-Moody Algebra G2H
• Arithmetic and Hyperbolic Structures in String Theory
• E11 and exceptional field theory
• Real forms of extended Kac-Moody symmetries and higher spin gauge theories
• Time-like T-duality algebra
• Poincare Duality and G+++ algebra's
• An M-theory solution from null roots in E11
• Some Algebraic Aspects of Half-BPS Bound States in M-Theory
• Kac-Moody Algebras in M-theory
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• E11 and Spheric Vacuum Solutions of Eleven- and Ten dimensional Supergravity Theories
• Bound States of String Theory and Beyond
• Killing Spinor Equations from Nonlinear Realisations
• The different faces of branes in Double Field Theory
• Hidden Symmetry Unmasked: Matrix Theory and E(11)
• An E11 invariant gauge fixing
• A Special Class of Rank 10 and 11 Coxeter Groups
• Higher spin fields from indefinite Kac-Moody algebras
• M-Theory Solutions in Multiple Signatures from E_11
• Infinite-Dimensional Gauge Structure of d=2 N=16 Supergravity
• Exceptional Lie algebras and M-theory
• Timelike duality, $M^{\prime }$-theory and an exotic form of the Englert solution
• The emergence of fermions and the E11 content
• Gravitational Coset Models
• Hidden Symmetries of M-Theory and Its Dynamical Realization
• A note on gauge fixing in supergravity/Kac-Moody correspondences
• Unifying R-symmetry in M-theory
• Gravitational Billiards, Dualities and Hidden Symmetries
• Algebraic structures in M-theory
• Massive Type IIA Supergravity and E10
• From brane dynamics to a Kac-Moody invariant formulation of M-theories
• String Dualities and Gaugings of Supergravity
• The Two-Parameter Brane Sigma-Model and Extended Solutions of M-Theory
• Gravitational theories coupled to matter as invariant theories under Kac-Moody algebras