Publication: G_2 generating technique for minimal D=5 supergravity and black rings

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Title G_2 generating technique for minimal D=5 supergravity and black rings
Authors/Editors* Adel Bouchareb, Chiang-Mei Chen, Gerard Clement, Dmitri V. Gal'tsov, Nikolai G. Scherbluk, Thomas Wolf
Where published* Phys. Rev. D, arXiv:0708.2361
How published* Journal
Year* 2007
Volume 76
Pages 104032
Keywords supergravity, black rings, Killing vectors, CRACK
A solution generating technique is developed for D=5 minimal supergravity with two commuting Killing vectors based on the G_2 U-duality arising in the reduction of the theory to three dimensions. The target space of the corresponding 3-dimensional sigma-model is the coset G_{2(2)}/(SL(2,R) x SL(2,R)). Its isometries constitute the set of solution generating symmetries. These include two electric and two magnetic Harrison transformations with the corresponding two pairs of gauge transformations, three SL(2,R) S-duality transformations, and the three gravitational scale, gauge and Ehlers transformations (altogether 14). We construct a representation of the coset in terms of 7 x 7 matrices realizing the automorphisms of split octonions. Generating a new solution amounts to transforming the coset matrices by one-parametric subgroups of G_{2(2)} and subsequently solving the dualisation equations. Using this formalism we derive a new charged black ring solution with two independent parameters of rotation.
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