Supersymmetric black rings and non-linear sigma models

In this paper we investigate the non-linear sigma model arising in the reduction of D = 5 supergravity to D = 3, and present the application of this sigma model to supersymmetric black ring solutions in five-dimensional minimal supergravity. With the ansatz of stationary solutions with R×U(1)×U(1) isometry, we obtain a two-dimensional Lagrangian corresponding to geodesic motion of a string-like object on the coset G2(+2)/SO(4), and study the algebra of conserved charges and supersymmetry constraints of supersymmetric black rings. We also obtain the semi-classical wave function of supersymmetric black rings.