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

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

2009-05-28

arxiv.org/abs/0905.4651v2

JHEP 0908:098,2009

Physics

High Energy Physics

High Energy Physics - Theory

70 pages, final version published in JHEP

Scientific paper

10.1088/1126-6708/2009/08/098

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.

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