@misc{BoucharebClementChenetal., author = {Bouchareb, Adel and Cl{\´e}ment, G{\´e}rard and Chen, Chiang-Mei and Wolf, Thomas and Gal'tsov, Dmitri V. and Scherbluk, Nikolai G.}, title = {G_2 generating technique for minimal D=5 supergravity and black rings}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11732}, number = {10-14}, 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.}, language = {en} }