Fuzzballs with internal excitations

We construct general 2-charge D1-D5 horizon-free non-singular solutions of IIB supergravity on T-4 and K3 described fuzzballs with excitations in the internal manifold; these excitations are characterized by arbitary curves. The solutions are obtained via dualities from F1-P solutions of heterotic and type IIB on T-4 for the K3 for the K3 and T-4 cases, respectively. We compute the holographic data encoded in these solutions, and show that the internal excitations are captured by vevs of chiral primaries associated with the middle cohomology and show that they indeed acquire vevs in the superpositions corresponding to fuzzballs with internal excitation, in accordance with the holographic results. We also address the question of whether the fuzzball program can be implemented consistently consistently within supergravity.