Holographic four-point functions in Toda field theories in AdS2

Abstract

Abstract We consider Toda field theories in a classical Euclidean AdS 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 $$ \mathcal{W} $$ W -algebras. Therefore we conjecture that the boundary operators are in one-to-one correspondence with the generators in the $$ \mathcal{W} $$ W -algebras.