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A triviality result in the AdS/CFT correspondence for Euclidean quantum fields with exponential interaction. (English) Zbl 1276.81100

Summary: 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.

MSC:

81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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