SL(4,R) generating symmetry in five-dimensional gravity coupled to dilaton and three-form

We give an explicit formulation of the three-dimensional SL(4,R)/SO(2,2) σ-model representing the five-dimensional Einstein gravity coupled to the dilaton and the three-form field for spacetimes with two commuting Killing vector fields. New matrix representation is obtained which is similar to one found earlier in the four-dimensional Einstein–Maxwell–Dilaton–Axion (EMDA) theory. The SL(4,R) symmetry joins a variety of 5D solutions of different physical types including strings, 0-branes, KK monopoles etc. interpreting them as duals to the four-dimensional Kerr metric translated along the fifth coordinate. The symmetry transformations are used to construct new rotating strings and composite (0–1)-branes endowed with a NUT parameter.