Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS Model

Abstract

The two-point functions of the energy-momentum tensor and the Noether current are used to probe the O(3) nonlinear sigma model in an energy range below 10^4 in units of the mass gap $m$. We argue that the form factor approach, with the form factor series trunctated at the 6-particle level, provides an almost exact solution of the model in this energy range. The onset of the (2-loop) perturbative regime is found to occur only at energies around $100m$.

13 pages LaTex, 4 PostScript figures; version published in Physics Letters B

References in corpus (5)

• Form Factors for Integrable Lagrangian Field Theories, the Sinh-Gordon Model
• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• Universal Properties of Self-Avoiding Walks from Two-Dimensional Field Theory
• Two-point Correlation Function in Integrable QFT with Anti-Crossing Symmetry
• Polynomial Form Factors in the O(3) Nonlinear sigma-Model

Cited by in corpus (11)

• Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond Monte-Carlo and Perturbation Theory
• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• Is the 2D O(3) Nonlinear $\sigma$ Model Asymptotically Free?
• The determinant representation for quantum correlation functions of the sinh-Gordon model
• The Intrinsic Coupling in Integrable Quantum Field Theories
• Questionable and unquestionable in the perturbation theory of non-Abelian models
• Nonlinear $\sigma$-model, form factors and universality
• The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model
• Two-point correlation functions in perturbed minimal models
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes
• Trans-series from condensates