4 matrix eigenvalues experience some quantum induced repulsion (similar to the VanderMonde repulsion of eigenvalues in matrix models [19]), arising from the volume of the gauge orbit of the configurations, and a confining potential due to the coupling to the curvature of the sphere (this is realized as an effective mass term for the eigenvalues). Repulsion wins at short distances, and the confining potential wins at long distances. Because of these competing effects one expects an equilibrium at finite radius and shape. In the large N thermodynamic limit the eigenvalues can form a geometric distribution that depends on the particular wave function of the system that is chosen. For the ground state, the wave function is known [5]. We will call this wave function ψ$_{0}$ . For this wave function the eigenvalue distribution is an S 5 submanifold of R $^{6}$, where the radius is of order √$_{N}$ in field theory units. Locality in S 5 is induced from locality in R $^{6}$: the masses of off-diagonal degrees of freedom depend on the distances between eigenvalues in R $^{6}$. Modes connecting nearby eigenvalues correspond to lighter degrees of freedom, whereas modes connecting distant eigenvalues correspond to very heavy degrees of freedom that decouple sooner. Hence the distance in R 6 is meaningfully describing a notion of locality: how coupled the different degrees of freedom are to each other when integrating out heavy fields. One can argue this way that this distribution describes the S 5 of the AdS$_{5}$ × S 5 dual geometry. Other supersymmetric wave functions are obtained by multiplying the ground state wave function with holomorphic polynomials of the variables, properly symmetrized between the eigenvalues. This type of argument has also been generalized to orbifolds [20, 21] and conifolds [22, 23], giving a large number of qualitative and quantitative tests of this idea. However, reproducing the exact geometry of supergravity from the field theory is still beyond the current understanding of the AdS/CFT dictionary. A particularly difficult question to answer is how different field theory degrees of freedom are encoded and localize in different parts of the AdS geometry, how the holographic bound is realized in practice [24] and in particular how to relate these questions to the holographic renormalization group [25, 26] (for a recent review see [27]). The upshot is that some geometric information can be extracted from these wave func- tions, but the said geometry contains only partial information about the full ten dimensional geometry that supergravity would see. Since to date there is no convincing way to extract the ten dimensional geometry directly from the field theory without assuming a correspon- dence, we will use the limited geometric information that can be derived from the field