The Maximal Abelian Gauge, Monopoles, and Vortices in SU(3) Lattice Gauge Theory

TL;DR

This paper investigates the effects of gauge fixing and projection methods on the heavy quark potential in SU(3) lattice gauge theory, highlighting the complexities of the maximal abelian gauge and proposing a generalized form.

Contribution

It introduces a generalized maximal abelian gauge for SU(3) and compares various gauge-fixing and projection techniques to full SU(3) results, revealing their impact on string tension calculations.

Findings

Projected string tensions are lower than full SU(3) tension.

Gauge ambiguities further reduce the projected string tensions.

Formulation of MAG for SU(3) is more complex than for SU(2).

Abstract

We report on calculations of the heavy quark potential in SU(3) lattice gauge theory. Full SU(3) results are compared to three cases which involve gauge-fixing and projection. All of these start from the maximal abelian gauge (MAG), in its simplest form. The first case is abelian projection to U(1)xU(1). The second keeps only the abelian fields of monopoles in the MAG. The third involves an additional gauge-fixing to the indirect maximal center gauge (IMCG), followed by center projection to Z(3). At one gauge fixing/configuration, the string tensions calculated from MAG U(1)xU(1), MAG monopoles, and IMCG Z(3) are all less than the full SU(3) string tension. The projected string tensions further decrease, by approximately 10%, when account is taken of gauge ambiguities. Comparison is made with corresponding results for SU(2). It is emphasized that the formulation of the MAG is more subtle for SU(3) than for SU(2), and that the low string tensions may be caused by the simple MAG form used. A generalized MAG for SU(3) is formulated.