Monopoles, vortices and confinement in SU(3) lattice gauge theory

Physics Letters B, 2001

We compute, in SU (3) pure gauge theory, the vacuum expectation value (vev) of the operator which creates a Z 3 vortex wrapping the lattice through periodic boundary conditions (dual Polyakov line). The technique used is the same already tested in the SU (2) case. The dual Polyakov line proves to be a good disorder parameter for confinement, and has a similar behaviour to the monopole condensate. The new features which characterise the construction of the disorder operator in SU (3) are emphasised.

We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. This is because we can define gauge-invariant magnetic monopoles which are inherent in the Wilson loop operator. For SU(3) there are two options: the minimal option with a single type of non-Abelian magnetic monopole characterized by the maximal stability subgroupH = U(2) = SU(2) ×U(1), and the maximal one with two types of Abelian magnetic monopoles characterized by the maximal torus subgroupH = U(1) × U(1). The maximal option corresponds to a gauge independent reformulation of the Abelian projection represented by the conventional MAG. In the minimal option, we have successfully performed the numerical simulation of the SU(3) Yang-Mills theory on a lattice. We give preliminary numerical results showing the dominance of the non-Abelian magnetic monopole in the string tension obtained from the Wilson loop in the fundamental representation, and the infrared dominance of a decomposed field variable for correlation functions after demonstrating the preservation of color symmetry which was explicitly broken by the conventional MAG.

Physical Review Letters, 2001

The static three-quark (3Q) potential is studied in SU(3) lattice QCD with 12 3 × 24 and β = 5.7 at the quenched level. From the 3Q Wilson loop, 3Q ground-state potential V3Q is extracted using the smearing technique for ground-state enhancement. With accuracy better than a few %, V3Q is well described by a sum of a constant, the two-body Coulomb term and the three-body linear confinement term σ3QLmin, with Lmin the minimal value of total length of color flux tubes linking the three quarks. Comparing with the Q-Q potential, we find a universal feature of the string tension, σ3Q ≃ σ QQ , and the OGE result for Coulomb coefficients, A3Q ≃ 1 2 A QQ .

Nuclear Physics B, 1992

We present numerical calculations using the magnetic monopoles of four-dimensional U(1) lattice gauge theory to obtain the heavy quark potential. Using the cosine action we perform a conventional gauge field simulation on a 16~lattice. We then use the DeGrand-Toussaint scheme for locating magnetic current in the lattice gauge field configurations to obtain our monopole configurations. In addition to the heavy quark potential we also calculate the potential between heavy external monopoles. In the confined phase of quarks, we observe total screening between external monopoles. In the Coulomb phase of the quarks we find a partially screened Coulomb potential between external monopoles. Under the assumptions used to obtain the potential between external monopoles, we verify that the Dirac quantization condition holds for the product of renormalized electric and magnetic charges.

Soryushiron Kenkyu Electronics, 2000

We outline a derivation of the area law of the Wilson loop in SU(3) Yang-Mills theory in the maximal Abelian gauge (The detailed exposition will be given in a forthcoming article). This derivation is performed within the reformulation of the Yang-Mills theory recently proposed by one of the authors. To this end, we extend a non-Abelian Stokes theorem to SU(3) by making use of the coherent state representation on the coset space SU(3)/(U(1)×U(1)) = F 2 , the flag space. Our results suggest that the fundamental quark is confined if G = SU(3) is broken by partial gauge fixing into H = U(2) rather than U(1) × U(1). An origin of the area law is related to the geometric phase of the Wilczek-Zee holonomy for U(2). Abelian dominance and magnetic monopole dominance are immediate byproduct of these results.

Proceedings of the Mongolian Academy of Sciences, 2020

In this work, we have studied SU(2) and SU(3) gauge theories explaining the colour interaction of a quark and an antiquark, and their identical and dissimilar properties. Using both gauge theories, we have performed simulations under similar conditions and have studied the differences in the results obtained. We have compared the transverse and longitudinal profiles of the chromoelectric and chromomagnetic components of the field strength, potential, and temperature-dependent string tension of the flux tube. The potential between the quark and antiquark of the SU(3) theory was larger than that of the SU(2) under all temperatures. The string tension of SU(3) tends to stabilize starting from the critical temperature while that of SU(2) has a gradual decreasing feature.

Dual superconductivity is believed to be a promising mechanism for quark confinement and has been investigated on a lattice effectively by a particular gauge called the maximal Abelian (MA) gauge. We propose a new formulation of SU(3) Yang-Mills theory on a lattice based on a non-linear change of variables where the new field variables are expected to reduce to those of the Cho-Faddeev-Niemi-Shabanov decomposition in the continuum limit. By introducing a new variable, say color field, carrying the color direction with it, this formulation enables us to restore and maintain color symmetry that was lost in the conventional MA gauge due to the naive separation of the gauge potential into diagonal and off-diagonal components. An advantage of this formulation is that we can define gaugeinvariant magnetic monopoles without relying on specific gauges to investigate quark confinement from the viewpoint of dual superconductivity. In this talk, we will present the relevant lattice formulation to realize the above advantages and preliminary results of numerical simulations to demonstrate the validity of this formulation. This SU(3) formulation is an extension of the SU(2) version already proposed by us in the previous conference.

The general problem of obtaining reliable results from gauge-fixing and projection is discussed. It is shown that the usual form of the maximal abelian gauge gives poor results for the string tension in SU(3) lattice gauge theory. A generalized form is suggested. Evidence is presented that monopoles in SU(3) are associated with SU(2) subgroups, and that P-vortices pass through monopoles, similar to what happens in SU(2).

AIP Conference Proceedings

We study the static three-quark (3Q) potential in detail using SU(3) lattice QCD with 12 3 × 24 at β = 5.7 and 16 3 × 32 at β = 5.8, 6.0 at the quenched level. For more than 200 patterns of the 3Q systems, we numerically derive 3Q ground-state potential V 3Q from the 3Q Wilson loop with the smearing technique, which reduces excited-state contaminations. The lattice QCD data of V 3Q are well reproduced within a few % deviation by a sum of a constant, the two-body Coulomb term and the three-body linear confinement term σ 3Q L min , with L min the minimal value of total length of color flux tubes linking the three quarks. From the comparison with the Q-Q potential, we find a universality of the string tension as σ 3Q σ QQ and the one-gluon-exchange result for Coulomb coefficients, A 3Q 1 2 A QQ .

Nuclear Physics B-proceedings Supplements, 1994

Calculations are presented which obtain the heavy quark potential using magnetic monopole current variables in U(1) and SU(2) lattice gauge theory. Very large loops of magnetic current are found in simulations of both theories. In the U(1) theory, calculations of the potential show that the large loops are entirely responsible for confinement.