A toy model for the AdS/CFT correspondence

We study the large N gauged quantum mechanics for a single Hermitian matrixin the Harmonic oscillator potential well as a toy model for the AdS/CFTcorrespondence. We argue that the dual geometry should be a string in twodimensions with a curvature of stringy size. Even though the dual geometry isnot weakly curved, one can still gain knowledge of the system from a detailedstudy of the open-closed string duality. We give a mapping between the basis ofstates made of traces (closed strings) and the eigenvalues of the matrix(D-brane picture) in terms of Schur polynomials. We connect this model with thestudy of giant gravitons in AdS_5 x S^5. We show that the two giant gravitonsthat expand along AdS_5 and S^5 can be interpreted in the matrix model astaking an eigenvalue from the Fermi sea and exciting it very much, or as makinga hole in the Fermi sea respectively. This is similar to recent studies of thec=1 string. This connection gives new insight on how to perform calculationsfor giant gravitons.Comment: 19 pages JHEP, 4 figures. v2: comments added, typos fixed, additional refs. v3: The paper has been largely revised, to make the relation as a limit of N=4 SYM clear, also some proofs have been written in full rather than sketched. This updated version reflects the changes that were made in the published versio