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arXiv · hep-lat/9412077

The Perturbative Method Fails in Non-Abelian Models

A. Patrascioiu·E. Seiler
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Abstract

It is shown that perturbation theory in $2D$ nonlinear $σ$-models as well gauge theories in dimension $D\geq 2$ produces answers that depend on boundary conditions even after the infinite volume limit has been taken. This unphysical phenomenon occurs only in the non-Abelian versions of those models, starting at $O(1/β^2)$. It is not present in the true (nonperturbatively defined) models and represents a failure of the perturbative method. It is related to a hitherto unnoticed type of low-lying excitation, dubbed super-instanton, that dominates the low-temperature (= weak coupling) regime of these models.

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A. Patrascioiu, E. Seiler. 1994-12-14. The Perturbative Method Fails in Non-Abelian Models. https://doi.org/10.1016/0920-5632(95)00393-n

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