Unquestionable in the Perturbation Theory of Nonabelian Models ∗

We show, by explicit computation, that bare lattice perturbation theory in the 2-dimensional O(n) nonlinear sigma–models with super– instanton boundary conditions is divergent in the limit of an infinite number of points |Λ|. This is the analogue of David’s statement that renormalized perturbation theory of these models is infra-red divergent in the limit where the physical size of the box tends to infinity. We also give arguments which support the validity of the bare perturbative expansion of short-distance quantities obtained by taking the limit |Λ| → ∞ term by term in the theory with more conventional boundary conditions such as Dirichlet, periodic and free. Work supported in part by Schweizerischer Nationalfonds On leave from the Institute of Theoretical Physics, Eötvös University, Budapest