Superinstantons in Gauge Theories and Troubles with Perturbation Theory

In gauge theories with continuous groups there exist classical solutions whose energy vanishes in the thermodynamic limit (in any dimension). The existence of these superinstantons 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 $O(1/{\beta }^2)$, and is expected to modify the universal coefficients of the $\beta$ function.