Adding momentum to supersymmetric geometries

We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a traveling wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1–D5 system on T⁴$T^4$. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1)$\mathrm{U}(1)$ current of the D1–D5 orbifold CFT on a given state.