Perturbations of W(infinity) CFTs
Matthias R. Gaberdiel, Kewang Jin, Wei Li
TL;DR
This work analyzes perturbations of W_infty-like CFTs that arise as the large-N limit of minimal models dual to higher-spin theories in AdS3. It identifies a marginal, symmetry-preserving perturbation that, to first order, introduces 1/N corrections without immediately breaking the W_infty symmetry, and it validates this construction through explicit free-field realizations at lambda = 0 and lambda = 1. The study develops a perturbative framework based on a mixing matrix and operator mixing in the 't Hooft limit, revealing a continuum of perturbed conformal weights organized by branches akin to edges of the Young lattice, and connects these results to finite-N corrections and to the continuous orbifold/coset pictures. Although the perturbation is not exactly marginal, it provides a controlled mechanism to interpolate between theories with different lambda and c, highlighting the role of light states and representation theory in governing deformations. Overall, the paper clarifies how 1/N-type corrections influence the W_infty symmetry and offers a concrete route to relate higher-spin CFTs to their stringy extensions.
Abstract
The holographic duals of higher spin theories on AdS_3 are described by the large N limit of a family of minimal model CFTs, whose symmetry algebra is equivalent to W(infinity)[lambda]. We study perturbations of these limit theories, and show that they possess a marginal symmetry-preserving perturbation that describes switching on the 1/N corrections. We also test our general results for the specific cases of lambda=0,1, where free field realisations are available.