  U($N$) supersymmetric Yang-Mills theory naturally appears as the low-energy
effective theory of a system of $N$ D-branes and open strings between them.
Transverse spatial directions emerge from scalar fields, which are $N\times N$
matrices with color indices; roughly speaking, the eigenvalues are the
locations of D-branes. In the past, it was argued that this simple 'emergent
space' picture cannot be used in the context of gauge/gravity duality, because
the ground-state wave function delocalizes at large $N$, leading to a conflict
with the locality in the bulk geometry. In this paper we show that this
conventional wisdom is not correct: the ground-state wave function does not
delocalize, and there is no conflict with the locality of the bulk geometry.
This conclusion is obtained by clarifying the meaning of the 'diagonalization
of a matrix' in Yang-Mills theory, which is not as obvious as one might think.
This observation opens up the prospect of characterizing the bulk geometry via
the color degrees of freedom in Yang-Mills theory, all the way down to the
center of the bulk.
