Large-N limits of 2d CFTs, Quivers and AdS_3 duals

TL;DR

This work analyzes large-$N$ limits of solvable 2d CFTs built from SU$(N)_k$ WZW models and their cosets, revealing two dual descriptions controlled by the 't Hooft-like coupling $\lambda=N/k$: a weakly coupled bosonic WZW regime and a strongly coupled fermionic/gauge regime with $N$ copies of massless Dirac fermions coupled to a $U(k)$ gauge group. It provides detailed spectral and four-point-function analyses, demonstrates the non-commutativity of large-$N$ and large-$\lambda$ limits, and connects these CFTs to holographic AdS$_3$ duals with open-string flavor sectors, modeled by Chern-Simons theories and a bulk scalar $T$ dual to the generating operator. The central results include a controlled bulk interpretation of ground states with large degeneracy, a mass-spectrum analysis showing a gravity-like gap at small $\lambda$ and a fully stringy bulk description at large $\lambda$, and a bulk effective action that reproduces CFT current correlators via boundary data. Overall, the paper uncovers a rich interplay between solvable 2d CFTs, level-rank dualities, and AdS$_3$ holography, highlighting how bulk descriptions must accommodate open-string flavor, horizonless states, and stringy exclusion in the strong-coupling regime.

Abstract

We explore the large-N limits of 2d CFTs, focusing mostly on WZW models and their cosets. The $SU(N)_k$ theory is parametrized in this limit by a 't Hooft-like coupling. We show a duality between strong coupling, where the theory is described by almost free fermions, and weak coupling where the theory is described by bosonic fields by an analysis of spectra and correlators. The AdS$_3$ dual is described, and several quantitative checks are performed. Besides the more standard states that should correspond to bulk black holes we find ground states with large degeneracy that can dominate the standard Cardy entropy at weak coupling and are expected to correspond to regular horizonless semiclassical bulk solutions.