The confining color field in SU(3) gauge theory

Abstract

We extend a previous numerical study of SU(3) Yang-Mills theory in which we measured the spatial distribution of all components of the color fields surrounding a static quark-antiquark pair for a wide range of quark-antiquark separations, and provided evidence that the simulated gauge invariant chromoelectric field can be separated into a Coulomb-like ‘perturbative’ field and a ‘non-perturbative’ field, identified as the confining part of the SU(3) flux tube field. In this paper we hypothesize that the fluctuating color fields not measured in our simulations do not contribute to the string tension. Under this assumption the string tension is determined by the color fields we measure, which form a tensor $F_{\mu \nu}$ pointing in a single direction in color space. We call this the Maxwell mechanism of confinement. We provide an additional procedure to isolate the non-perturbative (confining) field. We then extract the string tension from a stress energy-momentum tensor $T_{\mu \nu}$ having the Maxwell form, constructed from the non-perturbative part of the tensor $F_{\mu \nu}$ obtained from our simulations. To test our hypothesis we calculate the string tension from our simulations of the color fields for ten values of the quark-antiquark separation ranging from 0.37 fm to 1.2 fm. We also calculate the spatial distributions of the energy-momentum tensor $T_{\mu \nu}$ surrounding static quarks for this range of separations, and we compare these distributions with those obtained from direct simulations of the energy-momentum tensor in SU(3) Yang-Mills theory.

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