Abstract
It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS2 background are the same (up to a non-trivial proportionality coefficient) as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: boundary correlators of Toda scalars on AdS2 are directly related to the correlation functions of the chiral mathcal{W} -symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS2/CFT1 duality where the CFT1 is the chiral half of a 2d CFT; we shall to this as {mathrm{AdS}}_2/{mathrm{CFT}}_2^{raisebox{1ex}{1}!left/ !raisebox{-1ex}{2}right.} . In this paper we demonstrate that this duality applies also to the non-abelian Toda theory containing a Liouville scalar coupled to a 2d σ-model originating from the SL(2, ℝ)/U(1) gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor T while the other two scalars are dual to the parafermionic operators V± of the non-abelian Toda CFT. We explicitly check the duality at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of (T, V+, V−) (computed using a free field representation) with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS2.
Highlights
Like AdS2 to be directly related to the correlators in flat space
It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS2 background are the same as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line
The same relation generalizes to the conformal abelian Toda theory: boundary correlators of Toda scalars on AdS2 are directly related to the correlation functions of the chiral W-symmetry generators in the Toda CFT and are essentially controlled by the underlying infinite-dimensional symmetry
Summary
The generalization to abelian Toda theory for A2 and B2 algebras was discussed in [15]. Considering the AdS2 background (1.3) and expanding near the constant vacuum value for φ as in the Liouville theory (with φ0 given again by (1.4)) one can develop the perturbation theory in small b, i.e. in powers of the fluctuation fields ζ ≡ φ − φ0 and ψ These happen to have masses m2ζ = 2 and m2ψ = 6 corresponding (according to m2 = ∆(∆ − 1)) to the dual operator dimensions ∆ζ = 2 and ∆ψ = 3. Similar results should hold for higher rank abelian Toda models where there are more scalar fields with different masses corresponding to the higher-spin generators of the underlying W-algebra symmetry.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
