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Analyticity and causality in conformal field theory. (English) Zbl 1439.81082

Summary: We investigate analyticity properties of correlation functions in conformal field theories (CFTs) in the Wightman formulation. The goal is to determine domain of holomorphy of permuted Wightman functions. We focus on crossing property of three-point functions. The domain of holomorphy of a pair of three-point functions is determined by appealing to Jost’s theorem and by adopting the technique of analytic completion. This program paves the way to address the issue of crossing for the four-point functions on a rigorous footing.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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