Questionable and unquestionable in the perturbation theory of non-Abelian models

Abstract

We show, by explicit computation, that bare lattice perturbation theory in the two-dimensional O(n) nonlinear $\sigma$ models with superinstanton boundary conditions is divergent in the limit of an infinite number of points $|\Lambda |$. This is the analogue of David's statement that renormalized perturbation theory of these models is infrared divergent in the limit where the physical size of the box tends to infinity. We also give arguments which support the validity of the bare perturbative expansion of short-distance quantities obtained by taking the limit $|\Lambda |\to \infty$ term by term in the theory with more conventional boundary conditions such as Dirichlet, periodic, and free.

One reference added to the published version, 28 pages, 3 figures

References in corpus (6)

• A strong-coupling analysis of two-dimensional O(N) sigma models with N<=2 on square, triangular and honeycomb lattices
• Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models
• A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model
• Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS Model
• Comment on "Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models"
• Reply to David's Comment on ``Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models''

Cited by in corpus (12)

• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• Quasi-long-range ordering in a finite-size 2D Heisenberg model
• Questionable Arguments for the Correctness of Perturbation Theory in Non-Abelian Models
• Plaquette representation for 3D lattice gauge models: I. Formulation and perturbation theory
• Some new results on an old controversy: is perturbation theory the correct asymptotic expansion in nonabelian models?
• Low-temperature expansion and perturbation theory in 2D models with unbroken symmetry: a new approach
• Asymptotic Freedom and Finite-size Scaling of Two-dimensional Classical Heisenberg Model
• Spiral vortices in a 2D ferromagnet
• Exponential corrections to low-temperature expansion of 2D non-abelian models
• Low-temperature expansion in link formulation. II