Bootstrapping Pions at Large $N$

TL;DR

This paper applies modern bootstrap techniques to derive universal bounds on the effective field theory of massless pions in large N QCD, revealing features that may connect to hadronic phenomenology and suggesting QCD could sit at a critical boundary.

Contribution

It introduces a bootstrap approach to large N QCD, deriving bounds on pion effective theories and analyzing the geometry of these bounds with potential phenomenological implications.

Findings

Exclusion plots show a sharp kink potentially indicating the QCD point.

Universal bounds derived from positivity constraints on 2-to-2 scattering.

Partial analytic understanding of the bounds' geometry.

Abstract

We revisit from a modern bootstrap perspective the longstanding problem of solving QCD in the large $N$ limit. We derive universal bounds on the effective field theory of massless pions by imposing the full set of positivity constraints that follow from $2 \to 2$ scattering. Some features of our exclusion plots have intriguing connections with hadronic phenomenology. The exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that large $N$ QCD may sit at this kink. We critically examine this possibility, developing in the process a partial analytic understanding of the geometry of the bounds.