A triviality result in the AdS/CFT correspondence for Euclidean quantum fields with exponential interaction

We consider scalar quantum fields with exponential interaction on Euclidean hyperbolic space $\mathbb{H}^2$ in two dimensions. Using decoupling inequalities for Neumann boundary conditions on a tessellation of $\mathbb{H}^2$, we are able to show that the infra-red limit for the generating functional of the conformal boundary field becomes trivial.