Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4

Abstract

We study the symmetries of pure N=2 supergravity in D=4. As is known, this theory reduced on one Killing vector is characterised by a non-linearly realised symmetry SU(2,1) which is a non-split real form of SL(3,C). We consider the BPS brane solutions of the theory preserving half of the supersymmetry and the action of SU(2,1) on them. Furthermore we provide evidence that the theory exhibits an underlying algebraic structure described by the Lorentzian Kac-Moody group SU(2,1)^{+++}. This evidence arises both from the correspondence between the bosonic space-time fields of N=2 supergravity in D=4 and a one-parameter sigma-model based on the hyperbolic group SU(2,1)^{++}, as well as from the fact that the structure of BPS brane solutions is neatly encoded in SU(2,1)^{+++}. As a nice by-product of our analysis, we obtain a regular embedding of the Kac-Moody algebra su(2,1)^{+++} in e_{11} based on brane physics.

arXiv comment70 pages, final version published in JHEP

References in corpus (52)

• Unity of Superstring Dualities
• E_11 and M Theory
• E10 and a "small tension expansion" of M Theory
• $E_{11}$, SL(32) and Central Charges
• The E_{11} origin of all maximal supergravities
• Gauged Supergravities, Tensor Hierarchies, and M-Theory
• Very-extended Kac-Moody algebras and their interpretation at low levels
• Duality in linearized gravity
• E(11) and the Embedding Tensor
• Spacelike Singularities and Hidden Symmetries of Gravity
• Strongly Coupled Gravity and Duality
• Gravitational Duality, Branes and Charges
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• Universal BPS structure of stationary supergravity solutions
• The Symmetry of M-Theories
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Generating Geodesic Flows and Supergravity Solutions
• G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
• Intersection Rules for p-Branes
• A class of Lorentzian Kac-Moody algebras
• Representations of G+++ and the role of space-time
• Supersymmetry and Stationary Solutions in Dilaton-Axion Gravity
• E_11: Sign of the times
• Twistors and Black Holes
• Algebraic Aspects of Matrix Theory on T^d
• Quantum Attractor Flows
• Monopoles for Gravitation and for Higher Spin Fields
• Spectrum-generating Symmetries for BPS Solitons
• G+++ Invariant Formulation of Gravity and M-Theories: Exact Intersecting Brane Solutions
• An E9 multiplet of BPS states
• G2 Dualities in D=5 Supergravity and Black Strings
• E_{10} Symmetry in One-dimensional Supergravity
• Hyperbolic billiards of pure D=4 supergravities
• Non-linear parent action and dual gravity
• S-Duality for Linearized Gravity
• From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity
• Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
• From very-extended to overextended gravity and M-theories
• Constraints and the E10 Coset Model
• Supersymmetry and Gravitational Duality
• Local E(11)
• Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries
• Cosmological billiards and oxidation
• Supergravity description of spacetime instantons
• Dualities and signatures of G++ invariant theories
• Extended Symmetries in Supergravity: the Semi-simple Case
• Non-propagating degrees of freedom in supergravity and very extended G_2
• Poincare Duality and G+++ algebra's
• Can dual gravity be reconciled with E11?
• Time-like T-duality algebra

Cited by in corpus (7)

• G2 Dualities in D=5 Supergravity and Black Strings
• Extremal solutions of the S3 model and nilpotent orbits of G2(2)
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• A Riemann-Hilbert approach to rotating attractors
• Geroch Group Description of Black Holes
• "Flip" of SL(2,R)-duality in five-dimensional supergravity
• The NUT in the N=2 Superalgebra