Super-Instantons in Gauge Theories and Troubles with Perturbation Theory

Abstract

In gauge theories with continuous groups there exist classical solutions whose energy vanishes in the thermodynamic limit (in any dimension). The existence of these super-instantons is intimately related to the fact that even at short distances perturbation theory can fail to produce unique results. This problem arises only in non-Abelian models and only starting at O(1/beta^2).

9 pages, 1 figure available on request from the authors

References in corpus (2)

• On the Viability of Lattice Perturbation Theory
• Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models

Cited by in corpus (14)

• Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond Monte-Carlo and Perturbation Theory
• Asymptotic scaling in the two-dimensional $SU(3)$ $\sigma$-model at correlation length $4\times 10^5$
• Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model
• The Minimal Landau Background Gauge on the Lattice
• A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model
• A determination of the mass gap in the O(n) sigma model
• Questionable Arguments for the Correctness of Perturbation Theory in Non-Abelian Models
• Comment on "Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models"
• Plaquette representation for 3D lattice gauge models: I. Formulation and perturbation theory
• Low-temperature expansion and perturbation theory in 2D models with unbroken symmetry: a new approach
• Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit
• The Perturbative Method Fails in Non-Abelian Models
• Lattice artefacts and the running of the coupling constant
• External magnetic fields in gauge theories