Cutoff effects of Wilson fermions in the absence of spontaneous chiral symmetry breaking

TL;DR

This study investigates how Wilson fermions exhibit cutoff effects in two-dimensional QED without spontaneous chiral symmetry breaking, confirming theoretical predictions through numerical scaling tests.

Contribution

It provides the first numerical confirmation that non-chirality-breaking operators are O(a) improved in the chiral limit for Wilson fermions in this context.

Findings

Chiral symmetry is realized as Wigner in the continuum limit.

Vacuum expectation values of non-chirality-breaking operators are O(a) improved.

Numerical scaling tests confirm theoretical expectations.

Abstract

We simulate two dimensional QED with two degenerate Wilson fermions and plaquette gauge action. As a consequence of the Mermin-Wagner theorem, in the continuum limit chiral symmetry is realized a la Wigner. This property affects also the size of the cutoff effects. That can be understood in view of the fact that the leading lattice artifacts are described, in the continuum Symanzik effective theory, by chirality breaking terms. In particular, vacuum expectation values of non-chirality-breaking operators are expected to be O(a) improved in the chiral limit. We provide a numerical confirmation of this expectation by performing a scaling test.