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.

arXiv comment52+12 pages; 23 figures, v2: minor edits, references added

References in corpus (96)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Causality, Analyticity and an IR Obstruction to UV Completion
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• The Pomeron and Gauge/String Duality
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• SU(N) gauge theories at large N
• Large N_c in chiral perturbation theory
• Bootstrapping Mixed Correlators in the 3D Ising Model
• On the 1/N expansion in chiral perturbation theory
• The EFT-Hedron
• The wall of the cave
• Energy's and amplitudes' positivity
• The S-matrix Bootstrap I: QFT in AdS
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• String Theory and Quark Confinement
• Positivity Bounds for Scalar Theories
• Sharp Boundaries for the Swampland
• Extremal Effective Field Theories
• The Effective Theory of Long Strings
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• Softness and Amplitudes' Positivity for Spinning Particles
• Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• UV complete me: Positivity Bounds for Particles with Spin
• $K_{l4}$ - Decays Beyond One Loop
• Crossing Symmetric Dispersion Relations in QFTs
• Signs of Analyticity in Single-Field Inflation
• The S-matrix Bootstrap II: Two Dimensional Amplitudes
• Consistency of the Standard Model Effective Field Theory
• The pion-pion scattering amplitude
• Rigorous Limits on the Interaction Strength in Quantum Field Theory
• Quantum Gravity Constraints from Unitarity and Analyticity
• Massive Galileon Positivity Bounds
• Positivity Bounds for Massive Spin-1 and Spin-2 Fields
• Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints
• Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude
• Positivity bounds on vector boson scattering at the LHC
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• Positivity constraints on aQGC: carving out the physical parameter space
• Convex Geometry Perspective to the (Standard Model) Effective Field Theory Space
• Positivity of Curvature-Squared Corrections in Gravity
• The Chiral Lagrangian parameters, ${\overline{\ell }}_1$, ${\overline{\ell }}_2$, are determined by the $\rho$--resonance
• Into the EFThedron and UV constraints from IR consistency
• The Speed of Gravity
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Positivity in the sky
• Rigorous Bounds on Light-by-Light Scattering
• Dispersion Relation Bounds for pi pi Scattering
• ZZ and Zgamma still haven't found what they are looking for
• Vector Mesons and an Interpretation of Seiberg Duality
• Bounds on Amplitudes in Effective Theories with Massive Spinning Particles
• Flux Tube S-matrix Bootstrap
• The S-matrix Bootstrap IV: Multiple Amplitudes
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Carving out the Space of Open-String S-matrix
• Massive Spin-2 Scattering and Asymptotic Superluminality
• Positivity in Multi-Field EFTs
• Massive and Massless Spin-2 Scattering and Asymptotic Superluminality
• Positivity Constraints on Interacting Spin-2 Fields
• On Unitarity of Tree-Level String Amplitudes
• Generalized positivity bounds on chiral perturbation theory
• Adding flavour to the S-matrix bootstrap
• Towards a Theory of the QCD String
• Relative entropy in scattering and the S-matrix bootstrap
• The O(N) S-matrix Monolith
• 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
• Dual S-matrix Bootstrap I: 2D Theory
• A note on the S-matrix bootstrap for the 2d O(N) bosonic model
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• To Positivity and Beyond, where Higgs-Dilaton Inflation has never gone before
• QFT, EFT and GFT
• SUSY S-matrix Bootstrap and Friends
• Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Yang--Mills Glueballs as Closed Bosonic Strings
• Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering
• Selection rules for the S-Matrix bootstrap
• A model for pion-pion scattering in large-N QCD
• Large $N_c$ scaling of meson masses and decay constants
• Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
• Positivity in the effective field theory of cosmological perturbations
• Universal Bounds for SU(3) Low Energy Constants
• On the N-pion extension of the Lovelace-Shapiro model
• 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