Abstract
We find a large new class of explicit solutions preserving four supercharges in six-dimensional supergravity. The solutions are determined by solving a linear system of equations on a four-dimensional Kahler base studied by LeBrun. For particular choices of the parameters, we find regular backgrounds that are asymptotic to the near-horizon limit of the D1-D5-P black string. Holography implies that these backgrounds should be dual to 1/4-BPS states in the D1-D5-P CFT.
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