Fuzzball solutions for black holes and D1-brane-D5-brane microstates.

We revisit the relation between fuzzball solutions and D1-brane-D5-brane microstates. A consequence of the fact that the R ground states (in the usual basis) are eigenstates of the R charge is that only neutral operators can have nonvanishing expectation values on these states. We compute the holographic 1-point functions of the fuzzball solutions and find that charged chiral primaries have nonzero expectation values, except when the curve characterizing the solution is circular. The nonzero vacuum expectation values reflect the fact that a generic curve breaks R symmetry completely. This implies that fuzzball solutions (excepting circular ones) can only correspond to superpositions of R states and we give a proposal for the superposition corresponding to a given curve. We also address the question of what would be the geometric dual of a given R ground state.