Bubbling AdS and Vacuum String Field Theory

TL;DR

This paper establishes a correspondence between 1/2--BPS states in N=4 SYM and classical solutions in Vacuum String Field Theory, linking fermionic distributions to D-brane configurations and supergravity solutions.

Contribution

It introduces a novel mapping between BPS states and VSFT solutions using Wigner distributions and explores the implications of this correspondence for understanding supergravity and string theory.

Findings

BPS states correspond to VSFT solutions with a B-field as inverse Planck constant.

Pauli exclusion principle emerges from VSFT projector equations.

Coarse-graining maps fermionic droplets to supergravity solutions.

Abstract

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 VSFT D-branes. In this context the Pauli exclusion principle appears as a consequence of the VSFT 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.