Abelian Confinement Research Articles

String tensions in deformed Yang-Mills theory

We study k-strings in deformed Yang-Mills (dYM) with SU(N) gauge group in the semiclassically calculable regime on {mathbb{R}}^3times {mathbb{S}}^1 . Their tensions Tk are computed in two ways: numerically, for 2 ≤ N ≤ 10, and via an analytic approach using a re-summed perturbative expansion. The latter serves both as a consistency check on the numerical results and as a tool to analytically study the large-N limit. We find that dYM k-string ratios Tk/T1 do not obey the well-known sine- or Casimir-scaling laws. Instead, we show that the ratios Tk/T1 are bound above by a square root of Casimir scaling, previously found to hold for stringlike solutions of the MIT Bag Model. The reason behind this similarity is that dYM dynamically realizes, in a theoretically controlled setting, the main model assumptions of the Bag Model. We also compare confining strings in dYM and in other four-dimensional theories with abelian confinement, notably Seiberg-Witten theory, and show that the unbroken {mathbb{Z}}_N center symmetry in dYM leads to different properties of k-strings in the two theories; for example, a “baryon vertex” exists in dYM but not in softly-broken Seiberg-Witten theory. Our results also indicate that, at large values of N, k-strings in dYM do not become free.

Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD

We study strings between static quarks in QCD with ${n}_{f}$ adjoint fermions, including $\mathcal{N}=1$ supersymmetric Yang-Mills (SYM), in the calculable regime on ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{\mathbb{S}}_{L}^{1}$, which shares many features with the XY-spin model. We find that they have many qualitatively new features not previously known. The difference from other realizations of Abelian confinement is due to the composite nature of magnetic bions, whose Dirac quantum with fundamental quarks is two, and to the unbroken part of the Weyl group. In particular we show that strings are composed of two domain walls, that quarks are not confined on domain walls, that strings can end on domain walls, and that ``Y'' or ``$\mathrm{\ensuremath{\Delta}}$'' baryons can form. By similar argumentation, liberation of vortices on domain walls in the condensed matter counterparts may have important implications in the physics of transport. In the gauge theory we briefly discuss the lightest modes of strings and the decompactification limit.

Double-winding Wilson loops and monopole confinement mechanisms

We consider ``double-winding'' Wilson loops in SU(2) gauge theory. These are contours which wind once around a loop ${C}_{1}$ and once around a loop ${C}_{2}$, where the two co-planar loops share one point in common, and where ${C}_{1}$ lies entirely in (or is displaced slightly from) the minimal area of ${C}_{2}$. We discuss the expectation value of such double-winding loops in Abelian confinement pictures, where the spatial distribution of confining Abelian fields is controlled by either a monopole Coulomb gas, a caloron ensemble, or a dual Abelian Higgs model, and argue that in such models an exponential falloff in the sum of areas ${A}_{1}+{A}_{2}$ is expected. In contrast, in a center vortex model of confinement, the behavior is an exponential falloff in the difference of areas ${A}_{2}\ensuremath{-}{A}_{1}$. We compute such double-winding loops by lattice Monte Carlo simulation, and find that the area law falloff follows a difference-in-areas law. The conclusion is that even if confining gluonic field fluctuations are, in some gauge, mainly Abelian in character, the spatial distribution of those Abelian fields cannot be the distribution predicted by the simple monopole gas, caloron ensemble, or dual Abelian Higgs actions, which have been used in the past to explain the area law falloff of Wilson loops.

The abelian confinement mechanism revisited: New aspects of the Georgi–Glashow model

The confinement problem remains one of the most difficult problems in theoretical physics. An important step toward the solution of this problem is Polyakov’s work on abelian confinement. The Georgi–Glashow model is a natural testing ground for this mechanism which has been surprising us by its richness and wide applicability. In this work, we shed light on two new aspects of this model in 2+1 D. First, we develop a many-body description of the effective degrees of freedom. Namely, we consider a non-relativistic gas of W-bosons in the background of monopole–instanton plasma. Many-body treatment is a standard toolkit in condensed matter physics. However, we add a new twist by supplying the monopole–instantons as external background field. Using this construction along with a mean-field approximation, we calculate the form of the potential between two electric probes as a function of their separation. This potential is expressed in terms of the Meijer-G function which interpolates between logarithmic and linear behavior at small and large distances, respectively. Second, we develop a systematic approach to integrate out the effect of the W-bosons at finite temperature in the range 0≤T<MW, where MW is the W-boson mass, starting from the full relativistic partition function of the Georgi–Glashow model. Using a heat kernel expansion that takes into account the non-trivial thermal holonomy, we show that the partition function describes a three-dimensional two-component Coulomb gas. We repeat our analysis using the many-body description which yields the same result and provides a check on our formalism. At temperatures close to the deconfinement temperature, the gas becomes essentially two-dimensional recovering the partition function of the dual sine-Gordon model that was considered in a previous work.

Abelian dominance and the dual Meissner effect in local unitary gauges in SU(2) gluodynamics

Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we observe for the first time Abelian dominance in the confining part of the static potential in local unitary gauges such as the F12 gauge. We also study the flux-tube profile between the quark and antiquark in these local unitary gauges, and we find a clear signal of the dual Meissner effect. The Abelian electric field is found to be squeezed into a flux tube by the monopole supercurrent. This feature is the same as that observed in the nonlocal maximally Abelian gauge. These results suggest that the Abelian confinement scenario is gauge independent. Observing the important role of spacelike monopoles in the Polyakov gauge also indicates that the monopoles defined on the lattice do not necessarily correspond to those proposed by 't Hooft in the context of Abelian projection.

Abelian Confinement Mechanism and the QCD Vacuum

Abelian Confinement Mechanism and the QCD Vacuum

Abelian Confinement Mechanism and the QCD Vacuum

Abelian Confinement Mechanism and the QCD Vacuum

Abelian Confinement Mechanism in QCD

It is shown explicitly that quarks and gluons, dynamical as well as static, are confined in QCD if color magnetic monopoles in the abelian gauge condense. The mass generation essential fbr the confinement occurs from the spontaneous breaking of color magnetic Um(l) symmetry, whereas color electric Ue(l) remains unbroken.

Abelian Confinement Mechanism in QCD

Abelian Confinement Mechanism in QCD

Color flux and Yang-Mills structure-a dynamical model

In view of the basic difficulties of QCD to bring the confinement hypothesis to a calculational level, a field-theoretic flux tube model with local color gauge invariance is set up which exhibits triality confinement ab initio. This is achieved by an appropriate formulation of Gauss' law using the tube operator as canonical degree of freedom. Along the tube there are vectorlike gauge-invariant color excitations related to splitting and to the short-distance behavior. They receive their degrees of freedom from the tube oscillations and thus are a realization of Polyakov's program. The quarkless system averaged over the directions of the flux tubes passing through a given world point reproduces the pure Yang-Mills equations. The guide to the model is the loop-space formulation of the confining Gauss law of the abelian confinement theory. Basically we generalize to a nonabelian gauge structure not a local abelian field theory but directly the loop-space formulation of the abelian confinement theory.

Condensed Monopoles and Abelian Confinement

We show that contribution of monopole loops to the functional integral in four-dimensional lattice (quantum electrodynamics) can be mapped on to scalar quantum electro-dynamics. The phase transition where the monopole loops become very long then corresponds to the onset of the Higgs-Kibble mechanism and confinement due to the dual Meissner effect.