Dispersive CFT Sum Rules

Understand

We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory.

• We call a sum rule dispersive if it has double zeros at all double-twist operators above a fixed twist gap.
• Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity).
• They have been discussed using three seemingly different methods: analytic functionals dual to double-twist operators, dispersion relations in position space, and dispersion relations in Mellin space.