  It is interesting to ask: how does the radial space direction emerge from the
CFT in gauge-gravity duality? In this context we resolve a long-standing puzzle
with the gravity duals of two classes of states in the D1D5 CFT. For each class
the CFT states are in the untwisted sector, suggesting that the energy gap
should be $1/R_y$ where $R_y$ is the radius of the circle on which the D1D5 CFT
is compactified. For one class of states, the gravity dual indeed has exactly
this gap, while for the other class, the gravity dual has a very deep throat,
leading to an energy gap much smaller than $1/R_y$. We resolve this puzzle by
showing that for the latter class of states, perturbing the CFT off its free
point leads to the formation of a band structure in the CFT. We also explain
why such a band structure does not arise for the first class of states. Thus
for the case where a deep throat emerges in the gravity description, the
dynamics of falling down this throat is described in the CFT as a sequential
`hopping' between states all of which have the same energy at the free point;
this hopping amplitude converts an integer spaced spectrum into a closely
spaced band of energy levels.
