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

Understand

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).