Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-08-17
Phys.Rev.D76:104032,2007; Erratum-ibid.D78:029901,2008
Physics
High Energy Physics
High Energy Physics - Theory
21 pages revtex-4, 1 figure, typo corrected in Eq. (103)
Scientific paper
10.1103/PhysRevD.76.104032
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 $G_{2(2)}/(SL(2,R)\times SL(2,R))$. 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 $7\times 7$ 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 dualization equations. Using this formalism we derive a new charged black ring solution with two independent parameters of rotation.
Bouchareb Adel
Chen Chiang-Mei
Clement Gerard
Gal'tsov Dmitri V.
Scherbluk Nikolai G.
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