Isolating the confining color field in the SU(3) flux tube

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 quarkantiquark separations, and provided evidence that the simulated gauge invariant chromoelectric field can be separated into a Coulomb-like 'perturbative' field and a 'nonperturbative' 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 µν pointing in a single direction in color space. We call this the Maxwell mechanism of confinement.We provide an additional procedure to isolate the nonperturbative (confining) field. We then extract the string tension from a stress energy-momentum tensor T µν having the Maxwell form, constructed from the non-perturbative part of the tensor F µν 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 energymomentum tensor T µν surrounding static quarks for this range of separations, and we compare these distributions with those obtained from direct simulations of the energymomentum tensor in SU(3) Yang-Mills theory. a

Hybrid static potential flux tubes from SU(2) and SU(3) lattice gauge theory

“…While such flux tubes have been studied for the ordinary static potential using lattice gauge theory for quite some time (see refs. [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]), this is a rather new direction for hybrid static potentials, where first results appeared only recently [49][50][51][52]. In this paper we substantially extend existing work by performing computations for seven hybrid static potential sectors characterized by quantum numbers Λ ( )…”

The confining color field in SU(3) gauge theory

“…Recent times have witnessed an increasing numerical effort toward a more comprehensive numerical description of the color field around static sources, via the measurement of all components of both chromoelectric and chromomagnetic fields on all transverse planes passing through the line between the quarks [38]; of the spatial distribution of the stress energy-momentum tensor [39,40]; and the flux densities for hybrid static potentials [41,42]. A more complete numerical description of the color field around the sources brings improved visualization, enabling us to grasp features otherwise less visible.…”

“…In the numerical study [38] we simulated the spatial distribution in three dimensions of all components of the chromoelectric and chromomagnetic fields generated by a static quark-antiquark pair in pure SU(3) lattice gauge theory. We found that, although the components of the simulated chromoelectric field transverse to the line connecting the pair are smaller than the simulated longitudinal chromoelectric field, these transverse components are large enough to be fit to a Coulomb-like 'perturbative' field produced by two static sources parameterized by effective charges ±Q of the sources (see Eq.…”

“…As noted in [38], we can extract the value of the string tension from the non-perturbative field by utilizing the fact that the value of the chromoelectric field at the position of a quark is the force on the quark [43]. However, the Coulomb-like field (Eq.…”

Renormalizability of the center-vortex free sector of Yang-Mills theory

“…This phenomenon is associated with not only a linearly rising potential but also the formation of a flux tube (see Refs. [21,22] and references therein) with transverse collective modes [23,24]. This is a physical object on its own, which is well beyond the language of Green's functions and the usual Feynman diagrams.…”