Abstract.
Motivated by structural issues in the AdS-CFT correspondence, the theory of generalized free fields is reconsidered. A stress-energy tensor for the generalized free field is constructed as a limit of Wightman fields. Although this limit is singular, it fulfills the requirements of a conserved local density for the Poincaré generators. An explicit “holographic” formula relating the Klein-Gordon field on AdS to generalized free fields on Minkowski space-time is provided, and contrasted with the “algebraic” notion of holography. A simple relation between the singular stress-energy tensor and the canonical AdS stress-energy tensor is exhibited.
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Communicated by Klaus Fredenhagen
submitted 15/10/02, accepted: 24/06/03
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Dütsch, M., Rehren, KH. Generalized Free Fields and the AdS-CFT Correspondence . Ann. Henri Poincaré 4, 613–635 (2003). https://doi.org/10.1007/s00023-003-0141-9
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DOI: https://doi.org/10.1007/s00023-003-0141-9