  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.

High Energy Physics - Theory