Mixed Correlator Dispersive CFT Sum Rules
Abstract
Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to sum rules that suppress the double-twist sector of the spectrum and enjoy positivity properties at large twist. In this paper, we construct dispersive CFT functionals for correlators of unequal scalar operators in position- and Mellin-space. We then evaluate these functionals in the Regge limit to construct mixed correlator holographic CFT functionals which probe scalar particle scattering in Anti-de Sitter spacetime. Finally, we test properties of these dispersive sum rules when applied to the 3D Ising model, and we use truncated sum rules to find approximate solutions to the crossing equation.
Cite
@article{arxiv.2111.14731,
title = {Mixed Correlator Dispersive CFT Sum Rules},
author = {Anh-Khoi Trinh},
journal= {arXiv preprint arXiv:2111.14731},
year = {2022}
}
Comments
44+10 pages, 14 figures; v2: references added, fixed formatting