Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models

Physics – High Energy Physics – High Energy Physics - Lattice

Scientific paper

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8 pages, plain LaTeX, MPI-Ph/93-87 and AZPH-TH/93-33

Scientific paper

10.1103/PhysRevLett.74.1920

In dimension $D\leq 2$ the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton produces thermodynamic answers for the invariant Green's functions that differ from the standard ones, but only in non-Abelian models and only starting at $O(1/\beta^2)$. This effect modifies the $\beta$-function of the $O(N)$ models and persists in the large $N$ limit of the $O(N)$ models.

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