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.

70 pages, final version published in JHEP

References in corpus (11)

• The E_{11} origin of all maximal supergravities
• E(11) and the Embedding Tensor
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Universal BPS structure of stationary supergravity solutions
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
• Supersymmetry and Gravitational Duality
• Constraints and the E10 Coset Model
• Local E(11)
• Supergravity description of spacetime instantons
• Non-propagating degrees of freedom in supergravity and very extended G_2