  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 $R \times U(1)\times
U(1)$ isometry, we obtain a two-dimensional Lagrangian corresponding to
geodesic motion of a string-like object on the coset $G_{2(+2)}/SO(4)$, 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.
