TY - GEN
A1 - Bouchareb, Adel
A1 - Clément, Gérard
A1 - Chen, Chiang-Mei
A1 - Wolf, Thomas
A1 - Gal'tsov, Dmitri V.
A1 - Scherbluk, Nikolai G.
T1 - G_2 generating technique for minimal D=5 supergravity and black rings
N2 - 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.
T3 - ZIB-Report - 10-14
KW - supergravity
KW - black rings
KW - Killing vectors
KW - duality
Y1 - 2010
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1173
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-11732
SN - 1438-0064
ER -