Generalized free fields and the AdS-CFT correspondence

TL;DR

This paper explores generalized free fields within the AdS-CFT framework, constructing a stress-energy tensor as a limit of Wightman fields and providing a holographic relation between AdS and Minkowski space-time.

Contribution

It introduces a new approach to generalized free fields, including a stress-energy tensor construction and explicit holographic formulas relating AdS fields to Minkowski space.

Findings

Constructed a stress-energy tensor as a limit of Wightman fields.

Provided a holographic formula relating AdS Klein-Gordon fields to generalized free fields.

Demonstrated a relation between the singular stress-energy tensor and the canonical AdS stress-energy tensor.

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 fulfils the requirements of a conserved local density for the Poincar'e 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.