Abstract
We consider Toda field theories in a classical Euclidean AdS2 background. We compute the four-point functions of boundary operators in the a1, a2 and b2 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.
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