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The symmetry group on the Anti-de-Sitter space acts as a conformal group on its boundary. It is shown that quantum fields on Euclidean AdS – when restricted via suitable scaling – indeed fulfill conformal invariance on the boundary. Even in the case of non-interacting fields some new renormalization factors are required. In the case of interacting fields in AdS2 or fields with cut offs in arbitrary dimensions a new kind of somewhat intriguing infra-red problem arises. While the approach taken here does not reflect the richness of Maldacena’s AdS/CFT conjecture on supergravity and Yang-Mills theory, the AdS/CFT problem for Euclidean quantum fields allows the statement and proof of some rigorous results on the basis of what has been established in Constructive QFT.

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Hanno Gottschalk, Universität Wuppertal
Seminarraum Theoretische Physik
Contact: not specified