Strings on Bubbling Geometries

TL;DR

This paper explores the duality between gauge theory operators involving Schur polynomials and their string theory counterparts on bubbling AdS geometries, analyzing coherent states, entropy, and the BMN spectrum.

Contribution

It introduces a detailed analysis of coherent states and density matrices for operators on bubbling geometries, connecting gauge theory and string theory descriptions.

Findings

Coherent state wavefunctions are characterized for general Young tableaux.

A density matrix framework enables entropy calculations of operator ensembles.

The BMN string spectrum is recovered near any circle in the geometry.

Abstract

We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wavefunction.