The Perturbative Method Fails in Non-Abelian Models

Details The Perturbative Method Fails in Non-Abelian Models The Perturbative Method Fails in Non-Abelian Models

1994-12-14

arxiv.org/abs/hep-lat/9412077v1

Nucl.Phys.Proc.Suppl. 42 (1995) 826-828

Physics

High Energy Physics

High Energy Physics - Lattice

3 pages

Scientific paper

10.1016/0920-5632(95)00393-N

It is shown that perturbation theory in $2D$ nonlinear $\sigma$-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 $O(1/\beta^2)$. 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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