AdS_3/LCFT_2 - Correlators in Cosmological Topologically Massive Gravity
Daniel Grumiller, Ivo Sachs
TL;DR
This work tests the conjectured AdS$_3$/LCFT$_2$ duality for cosmological topologically massive gravity at the chiral point by deriving momentum-space 2- and 3-point correlators from the bulk theory. The authors develop a complete classification of linearized solutions in global AdS$_3$, including normalizable and non-normalizable left, right, and logarithmic modes organized into $SL(2,\,\mathbb{R})$ representations, and compute correlators from the second and third variations of the action. They demonstrate that the resulting 2-point functions vanish or double in the expected way for the LCFT with $c_L=0$, while logarithmic modes yield finite, analytic momentum-space correlators, and they confirm that 3-point functions match LCFT predictions. Overall, the results provide robust gravity-side evidence that CTMG at the chiral point is dual to a logarithmic CFT and lay groundwork for an explicit AdS$_3$/LCFT$_2$ dictionary with potential applications to strongly coupled LCFTs and related holographic models.
Abstract
For cosmological topologically massive gravity at the chiral point we calculate momentum space 2- and 3-point correlators of operators in the postulated dual CFT on the cylinder. These operators are sourced by the bulk and boundary gravitons. Our correlators are fully consistent with the proposal that cosmological topologically massive gravity at the chiral point is dual to a logarithmic CFT. In the process we give a complete classification of normalizable and non-normalizeable left, right and logarithmic solutions to the linearized equations of motion in global AdS_3.