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

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.

11 pages; a new section (sec. V) added; match the published version

References in corpus (7)

• Asymptotic safety guaranteed
• Finite-size scaling at first-order quantum transitions
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Percolation of Vortices in the 3D Abelian Lattice Higgs Model
• Three-dimensional lattice SU($N_c$) gauge theories with multiflavor scalar fields in the adjoint representation
• Gauge fixing and gauge correlations in noncompact Abelian gauge models
• Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement