Symanzik effective actions in the large N limit

TL;DR

This paper derives Symanzik effective actions for certain lattice regularizations of the 2D non-linear O(N) sigma model in the large N limit, including non-classical cases, confirming their accuracy in predicting lattice artifacts.

Contribution

It provides the first derivation of Symanzik effective actions for a class of lattice regularizations beyond classical limits in the large N limit.

Findings

Effective actions reproduce known lattice artifacts.

Includes actions without classical limits.

Supports Symanzik's theory of lattice artifacts.

Abstract

Symanzik effective actions, conjectured to describe lattice artifacts, are determined for a class of lattice regularizations of the non-linear O(N) sigma model in two dimensions in the leading order of the 1/N-expansion. The class of actions considered includes also ones which do not have the usual classical limit and are not (so far) treatable in the framework of ordinary perturbation theory. The effective actions obtained are shown to reproduce previously computed lattice artifacts of the step scaling functions defined in finite volume, giving further confidence in Symanzik's theory of lattice artifacts.