Sum Rules from an Extra Dimension

Abstract

Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green's functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning their large and small frequency behavior and their pole structure. From these results, it is straightforward to prove the validity of various sum rules on the field theory side of the duality. We introduce a novel contraction mapping we use to study the large frequency behavior of the Green's functions.

v2: 23 pages (plus appendix), revised presentation, discussion of branch cuts moved to appendix, and some minor changes; v1: 24 pages (plus appendix)

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