Mixed Correlator Dispersive CFT Sum Rules

TL;DR

This paper develops dispersive sum rules for unequal scalar correlators in conformal field theories, enabling the analysis of crossing symmetry and holographic scattering, with applications to the 3D Ising model.

Contribution

It introduces dispersive CFT functionals for unequal scalar operators and applies them to holographic CFTs and the 3D Ising model, advancing the understanding of correlator reconstruction.

Findings

Constructed dispersive functionals for mixed scalar correlators.

Applied sum rules to the 3D Ising model for approximate solutions.

Probed scalar scattering in AdS via Regge limit analysis.

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.