Modified Abelian and SU(2) Wilson theories on a lattice from a non-compact regularization

TL;DR

This paper develops a noncompact regularization approach for Abelian and SU(2) Wilson gauge theories on a lattice, aiming to improve the physical volume and computational aspects of lattice gauge simulations.

Contribution

It introduces a noncompact regularization for U(1) gauge theories and extends the noncompact formulation to SU(2), enhancing the understanding of gauge invariance and simulation efficiency.

Findings

Noncompact U(1) regularization derived.

SU(2) noncompact formulation yields larger physical volume.

Auxiliary field coupling may simplify fermion matrix inversion.

Abstract

Multiflavor gauge theories of matter systems on a three-dimensional lattice have recently been widely investigated especially in connection with a possible symmetry enlargement at a continuous phase transition. Abelian models were studied both with compact gauge fields and in a mixed formulation in which the coupling with matter fields is in compact form while the gauge fields Lagrangian is written in terms of noncompact gauge fields, getting quite different results. Such a mixed formulation is not permissible for non-Abelian theories, for which however there exists an entirely noncompact formulation (in which exact gauge invariance is enforced by help of auxiliary fields), which for SU(2) was shown to yield in the scaling window a larger physical volume than Wilson's one. The corresponding U(1) noncompact regularization is derived in the present work. In both Abelian and SU(2) cases there is only one auxiliary field that for a large mass has a linear coupling with the other fields and it can be integrated out yielding a negative definite correction. The coupling with the auxiliary field might make the inversion of the fermion matrix easier.