Effective Coulomb potential in SU(3) lattice Yang-Mills theory

Abstract

We study the infrared behavior of the effective Coulomb potential in lattice SU(3) Yang-Mills theory in the Coulomb gauge. We use lattices up to a size of 48(4) and three values of the inverse coupling, beta=5.8, 6.0, and 6.2. While finite-volume effects are hardly visible in the effective Coulomb potential, scaling violations and a strong dependence on the choice of Gribov copy are observed. We obtain bounds for the Coulomb string tension that are in agreement with Zwanziger's inequality relating the Coulomb string tension to the Wilson string tension

Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

“…This ultraviolet behavior was confirmed by earlier lattice calculations [41]- [43]. However, the most recent numerical evaluation [44] contradicts these earlier findings.…”

Coulomb flux tube on the lattice

“…For convenience we take R R R 1 to be the origin, and R R R 2 = R R R = Rê e e x to lie along the x-axis. It is well known from lattice simulations [10][11][12][13][14][15] that V C (R) is a linearly confining potential. What has not been investigated up to now is the spatial distribution of the color Coulomb field which gives rise to this potential.…”

Coulomb string tension, asymptotic string tension, and the gluon chain

“…We have calculated the instantaneous Coulomb potential by the method just described on a 24 4 hypercubic lattice in SU(3) pure gauge theory with a standard Wilson action and lattice coupling β in the range β ∈ [5.9, 6.4]. The method of Fourier acceleration is used for Coulomb gauge fixing [5].…”

“…To convert everything to physical units we divide both sides by the lattice spacing a(β ) and multiply by a conversion factor (0.197 Gev-fm = 1) taking inverse fm to 2 These authors find a Coulomb string tension which is 2.2 [3] or 1.6 [4] times the asymptotic string tension. Our result, reported in the next section, is substantially higher than those values.…”

“…[3] for SU (2) and in ref. [4] for SU(3) gauge groups, which is to directly compute the expectation value of the operator K(x x x − y y y, A), Fourier transformed to momentum space. This involves inverting the FaddeevPopov operator M = −∇ · D(A), and looking for a plateau in k 4 V (k).…”