Poincare Duality and G+++ algebra's

Abstract

Theories with General Relativity as a sub-sector exhibit enhanced symmetries upon dimensional reduction, which is suggestive of ``exotic dualities''. Upon inclusion of time-like directions in the reductions one can dualize to theories in different space-time signatures. We clarify the nature of these dualities and show that they are well captured by the properties of infinite-dimensional symmetry algebra's (G+++ algebra's), but only after taking into account that the realization of Poincare duality leads to restrictions on the denominator subalgebra appearing in the non-linear realization. The correct realization of Poincare duality can be encoded in a simple algebraic constraint, that is invariant under the Weyl-group of the G+++ algebra, and therefore independent of the detailed realization of the theory under consideration. We also construct other Weyl-invariant quantities that can be used to extract information from the G+++ algebra without fixing a level decomposition.

47 pages, 5 figures, LaTeX

References in corpus (34)

• Target Space Duality in String Theory
• E_11 and M Theory
• Timelike T-Duality, de Sitter Space, Large $N$ Gauge Theories and Topological Field Theory
• E10 and a "small tension expansion" of M Theory
• Duality and the Signature of Space-Time
• $E_{11}$, SL(32) and Central Charges
• Very-extended Kac-Moody algebras and their interpretation at low levels
• Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity
• The Symmetry of M-Theories
• Higher-dimensional Origin of D=3 Coset Symmetries
• G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
• Branes, Times and Dualities
• A class of Lorentzian Kac-Moody algebras
• E_{11} origin of Brane charges and U-duality multiplets
• E_11: Sign of the times
• Duality and Moduli Spaces for Time-Like Reductions
• Euclidean-signature Supergravities, Dualities and Instantons
• The group theory of oxidation
• Finite in All Directions
• Kleinian Geometry and the N=2 Superstring
• The group theory of oxidation II: Cosets of non-split groups
• G+++ Invariant Formulation of Gravity and M-Theories: Exact Intersecting Brane Solutions
• Brane dynamics, central charges and E_{11}
• Hidden Symmetries and Dirac Fermions
• From very-extended to overextended gravity and M-theories
• The topology of U-duality (sub-)groups
• G+++ and Brane Solutions
• Dualities and signatures of G++ invariant theories
• Time-like T-duality algebra
• E11 and Spheric Vacuum Solutions of Eleven- and Ten dimensional Supergravity Theories
• U-duality (sub-)groups and their topology
• Killing Spinor Equations from Nonlinear Realisations
• On the construction of variant supergravities in D=11, D=10
• M-Theory Solutions in Multiple Signatures from E_11

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• Arithmetic and Hyperbolic Structures in String Theory
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• Kac-Moody Algebras in M-theory
• The Two-Parameter Brane Sigma-Model and Extended Solutions of M-Theory
• Symmetries of non-maximal supergravities with higher-derivative corrections