Generating technique for $U(1)^3 5D$ supergravity

Understand

We develop generating technique for solutions of $U(1)^3 5D$ supergravity via dimensional reduction to three dimensions.

• This theory, which recently attracted attention in connection with black rings, can be viewed as consistent truncation of the $T^6$ compactification of the eleven-dimensional supergravity.
• Its further reduction to three dimensions accompanied by dualisation of the vector fields leads to 3D gravity coupled sigma model on the homogeneous space $SO(4,4)/SO(4)\times SO(4)$ or $SO(4,4)/SO(2,2)\times SO(2,2)$ depending on the signature of the three-space.
• We construct a $8\times 8$ matrix representation of these cosets in terms of lower-dimensional blocks.