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arXiv · 0708.2361

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

Adel Bouchareb·Chiang-Mei Chen·Gerard Clement·Dmitri V. Gal'tsov·Nikolai G. Scherbluk·Thomas Wolf
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Abstract

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.

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Adel Bouchareb, Chiang-Mei Chen, Gerard Clement, Dmitri V. Gal'tsov, Nikolai G. Scherbluk, Thomas Wolf. 2008-06-07. $G_2$ generating technique for minimal D=5 supergravity and black rings. https://doi.org/10.1103/physrevd.76.104032%2010.1103%2Fphysrevd.78.029901

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