High Energy Theory Seminar

I will motivate and discuss the notion of dispersive sum rules in conformal field theory. These sum rules constitute nonperturbative constraints on the OPE data and follow from the conformal crossing equation. The adjective "dispersive" means the sum rules suppress all double-twist operators above a fixed twist. This property makes the sum rules ideally suited for implementing the analytic bootstap, in particular in holographic CFTs. I will explain that dispersive sum rules can be derived using several equivalent approaches: analytic functionals applied to the conformal crossing equation, superconvergence sum rules, and dispersion relations in position space or Mellin space. The talk will be based on https://arxiv.org/pdf/2008.04931.pdf.