Dynamical evolution in the D1D5 CFT

TL;DR

This paper investigates how the radial space emerges in the D1D5 CFT within gauge-gravity duality, resolving a long-standing puzzle about the energy gap differences in gravity duals of different CFT states.

Contribution

It demonstrates how perturbations off the free point in the CFT lead to band structures and deep throats in gravity duals, explaining the emergence of the radial direction.

Findings

Deep throat formation correlates with a band structure in the CFT.

Perturbing the CFT off its free point causes hopping between states.

Energy gaps differ based on the class of CFT states.

Abstract

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.