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

References in corpus (34)

• Causality, Analyticity and an IR Obstruction to UV Completion
• The Pomeron and Gauge/String Duality
• SU(N) gauge theories at large N
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• The EFT-Hedron
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Sharp Boundaries for the Swampland
• Extremal Effective Field Theories
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Crossing Symmetric Dispersion Relations in QFTs
• Positivity of Curvature-Squared Corrections in Gravity
• Into the EFThedron and UV constraints from IR consistency
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Rigorous Bounds on Light-by-Light Scattering
• Dispersion Relation Bounds for pi pi Scattering
• Vector Mesons and an Interpretation of Seiberg Duality
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Positivity in Multi-Field EFTs
• On Unitarity of Tree-Level String Amplitudes
• Causality, Unitarity and Symmetry in Effective Field Theory
• The Other Fermion Compositeness
• Quantum field theory and the Bieberbach conjecture
• Triple crossing positivity bounds for multi-field theories
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• QFT, EFT and GFT
• Yang--Mills Glueballs as Closed Bosonic Strings
• Selection rules for the S-Matrix bootstrap
• Universal Bounds for SU(3) Low Energy Constants
• NNLO Positivity Bounds on Chiral Perturbation Theory for a General Number of Flavours
• Spin and flavor projection operators in the $SU(2N_f)$ spin-flavor group

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