Spinning dispersive CFT sum rules and bulk scattering
arXiv:2311.04271
Abstract
We use commutativity of null-integrated operators on the same null plane to construct dispersive CFT sum rules for spinning operators. The contribution of heavy blocks to these sum rules is dominated by a saddle configuration that we call the "scattering crystal." Correlators in this configuration have a natural flat-space interpretation, which allows us to build a dictionary between dispersive CFT sum rules for stress-tensors and flat-space dispersion relations for gravitons. This dictionary is a crucial step for establishing the HPPS conjecture for stress tensor correlators.
54 pages + appendices, 7 figures; v2: added references and fixed typos; v3: updated discussion of remaining steps for uplifting flat space bounds to AdS