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

Abstract

We revisit the relation between fuzzball solutions and D1-D5 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 non-vanishing expectation values on these states. We compute the holographic 1-point functions of the fuzzball solutions and find that charged chiral primaries have non-zero expectation values, except when the curve characterizing the solution is circular. The non-zero vevs 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.