Bootstrapping Pions at Large $N$

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.

52+12 pages; 23 figures, v2: minor edits, references added

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Cited by in corpus (10)

• Graviton partial waves and causality in higher dimensions
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Bell inequalities in 2-2 scattering
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Bounds on photon scattering
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Positivity bounds at one-loop level: the Higgs sector