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.
Highlights
(Here we have assumed that Φ is W∞[λ] primary.) Given that the WN,k minimal models are not expected to have any such perturbation — the integrable perturbation by the field (0; adj) is relevant and induces the RG flow from k → k − 1 — we can only hope to find a solution to this problem either at generic values of (λ, c) of the W∞[λ] theory, or in the ’t Hooft limit of the WN,k models
In the ’t Hooft limit the ratio ∆D/N (as well as the drift term (λ2B− − 1)/N ) become continuous variables, and the branches of minimal model representations lead to a continuum of perturbed conformal dimensions; this matches the continuum for ρ we found above
In this paper we have studied the behaviour of the W∞[λ] theories under perturbations that preserve the symmetry algebra to first order
Summary
Let us consider the theory of N free complex fermions ψi and ψ∗i, i = 1, . With similar expressions for the right movers ψi and ψ∗j. We shall always consider only states that are singlets with respect to the global SU(N ) action. The free theory has the conserved spin-s chiral currents [25, 26, 27] (the expressions for the anti-chiral currents are analogous) s−1. ∂s−1−kψ∗i ∂kψi , k k=0 where the sum over i is implicit, and we choose the normalisation convention (2.4)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
