Bubbling AdS and vacuum string field theory

We show that a family of 1/2-BPS states of N = 4 SYM is in correspondence with a family of classical solutions of VSFT with a B-field playing the role of the inverse Planck constant. We show this correspondence by relating the Wigner distributions of the N fermion systems representing such states, to low energy space profiles of systems of VSFF D-branes. In this context the Pauli exclusion principle appears as a consequence of the VSIFT projector equation. The family of 1/2-BPS states maps through coarse-graining to droplet LLM supergravity solutions. We discuss the possible meaning of the corresponding coarse graining in the VSFT side. (c) 2006 Elsevier B.V. All rights reserved.