Holographic four-point functions in Toda field theories in AdS 2

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 W\[ \mathcal{W} \]-algebras. Therefore we conjecture that the boundary operators are in one-to-one correspondence with the generators in the W\[ \mathcal{W} \]-algebras.