Holographic four-point functions in Toda field theories in $Ad{S}_2$

Abstract

We consider Toda field theories in a classical Euclidean $Ad{S}_2$ background. We compute the four-point functions of boundary operators in the $a_1$, $a_2$ and $b_2$ Toda field theories. They take the same form as the four-point functions of generators in the corresponding $\mathcal{W}$-algebras. Therefore we conjecture that the boundary operators are in one-to-one correspondence with the generators in the $\mathcal{W}$-algebras.

arXiv comment14 pages

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• Boundary correlators in WZW model on AdS${}_2$
• Toda theory in AdS${}_2$ and $\mathcal{W}{A}_n$-algebra structure of boundary correlators
• Notes on $n$-point Witten diagrams in AdS${}_2$