We construct an infinite family of asymptotically flat 3-charge solutions carrying D1, D5 and momentum charges. Generically the solutions also carry two angular momenta. The geometries describe the spectral flow of all the ground states of the D1–D5 CFT. The family is parametrized by four functions describing the embedding of a closed curve in R4 and an integer n labelling the spectral flow on the left sector. After giving the general prescription for spectral flowing any of the ground states, we give an explicit example of the construction. We identify the asymptotic charges of the resulting solution and show the matching with the corresponding CFT result.
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