G2 generating technique for minimal D=5 supergravity and black rings

A solution-generating technique is developed for D=5 minimal supergravity with two commuting Killing vectors based on the G2 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 G2(2)/[SL(2,R)×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 7×7 matrices realizing the automorphisms of split octonions. Generating a new solution amounts to transforming the coset matrices by one-parametric subgroups of G2(2) and subsequently solving the dualization equations. Using this formalism we derive a new charged black ring solution with two independent parameters of rotation.