A toy model for the AdS/CFT correspondence

TL;DR

This paper presents a simplified matrix quantum mechanics model as a toy for the AdS/CFT correspondence, exploring open-closed string duality, eigenvalue dynamics, and giant graviton interpretations.

Contribution

It introduces a novel matrix model mapping between trace states and eigenvalues, connecting giant gravitons with Fermi sea excitations, and offers insights into string dualities in a simplified setting.

Findings

Mapping between trace states and eigenvalues via Schur polynomials

Interpretation of giant gravitons as eigenvalue excitations or holes in the Fermi sea

Insights into open-closed string duality in a non-weakly curved geometry

Abstract

We study the large N gauged quantum mechanics for a single Hermitian matrix in the Harmonic oscillator potential well as a toy model for the AdS/CFT correspondence. We argue that the dual geometry should be a string in two dimensions with a curvature of stringy size. Even though the dual geometry is not weakly curved, one can still gain knowledge of the system from a detailed study of the open-closed string duality. We give a mapping between the basis of states made of traces (closed strings) and the eigenvalues of the matrix (D-brane picture) in terms of Schur polynomials. We connect this model with the study of giant gravitons in AdS_5 x S^5. We show that the two giant gravitons that expand along AdS_5 and S^5 can be interpreted in the matrix model as taking an eigenvalue from the Fermi sea and exciting it very much, or as making a hole in the Fermi sea respectively. This is similar to recent studies of the c=1 string. This connection gives new insight on how to perform calculations for giant gravitons.