Vortices and confinement in hot and cold <i>D</i> = 2+1 gauge theories

Hart, Alistair; Lucini, Biagio; Teper, M.; Schram, Zsolt

doi:10.1088/1126-6708/2000/06/040

Cited by 20 publications

(34 citation statements)

References 6 publications

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“…We see that our results in eqn (24) and eqn (25) are consistent, at the 2σ level, with both these expectations, within quite small errors; with perhaps a slight bias towards favouring MQCD. It is because the two sets of predictions are numerically very similar that we cannot, at present, choose between them.…”

Section: K-strings In D=3+1supporting

confidence: 86%

“…Another interesting question is how the string tension ratios, whether given by MQCD or Casimir scaling, reflect themselves in k-vortex condensates, in the dual disorder loop approach to confinement [28], and whether this exposes any simple duality between Wilson loops and 't Hooft disorder loops. A calculation, illustrating how one might proceed, was outlined in [5,24]. A similar question can be posed in monopole models of confine-ment, following upon the simple model calculations of higher charged string tensions in [29], after Abelian projection, and in [27] with adjoint monopoles (at high T ).…”

Section: Discussionmentioning

confidence: 99%

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Confining strings inSU(N)gauge theories

2001

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We calculate the string tensions of k-strings in SU(N) gauge theories in both 3 and 4 dimensions. We do so for SU(4) and SU(5) in D=3+1, and for SU(4) and SU(6) in D=2+1. In D=3+1, we find that the ratio of the k = 2 string tension to the k = 1 fundamental string tension is consistent, at the 2σ level, with both the M(-theory)QCDinspired conjecture that σ k ∝ sin(πk/N) and with 'Casimir scaling', σ k ∝ k(N − k). In D=2+1, where our results are very precise, we see a definite deviation from the MQCD formula, as well as a much smaller but still significant deviation from Casimir scaling. We find that in both D=2+1 and D=3+1 the high temperature spatial k-string tensions also satisfy approximate Casimir scaling. We point out that approximate Casimir scaling arises naturally if the cross-section of the flux tube is nearly independent of the flux carried, and that this will occur in an effective dual superconducting description, if we are in the deep-London limit. We estimate, numerically, the intrinsic width of k-strings in D=2+1 and indeed find little variation with k. In addition to the stable k-strings we investigate some of the unstable strings, which show up as resonant states in the string mass spectrum. While in D=3+1 our results are not accurate enough to extract the string tensions of unstable strings, our more precise calculations in D=2+1 show that there the ratios between the tensions of unstable strings and the tension of the fundamental string are in reasonably good agreement with (approximate) Casimir scaling. We also investigate the basic assumption that confining flux tubes are described by an effective string theory at large distances, and attempt to determine the corresponding universality class. We estimate the coefficient of the universal Lüscher correction from periodic strings that are longer than 1 fermi, and find c L = 0.98(4) in the D=3+1 SU(2) gauge theory and c L = 0.558(19) in D=2+1. These values are within 2σ of the simple bosonic string values, c L = π/3 and c L = π/6 respectively, and are inconsistent with other simple effective string theories such as fermionic, supersymmetric or Neveu-Schwartz.

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Section: K-strings In D=3+1supporting

confidence: 86%

Section: Discussionmentioning

confidence: 99%

Confining strings inSU(N)gauge theories

2001

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“…A precise relationship between such a gauge-fixed, so called P-vortices and the topological center vortices originally introduced by 't Hooft[52] is still missing. The interested reader is referred to Refs [53][54][55][56][57][58][59][60][61][62][63][64][65]. for further discussions on the subject.…”

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confidence: 99%

Coulomb versus physical string tension on the lattice

et al. 2015

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From continuum studies it is known that the Coulomb string tension σC gives an upper bound for the physical (Wilson) string tension σW [1]. How does however such relationship translate to the lattice? In this paper we give evidence that there, while the two string tensions are related at zero temperature, they decouple at finite temperature. More precisely, we show that on the lattice the Coulomb gauge confinement scenario is always tied to the spatial string tension, which is known to survive the deconfinement phase transition and to cause screening effects in the quark-gluon plasma. Our analysis is based on the identification and elimination of center vortices which allows to control the physical string tension and study its effect on the Coulomb gauge observables. We also show how alternative definitions of the Coulomb potential may sense the deconfinement transition; however a true static Coulomb gauge order parameter for the phase transition is still elusive on the lattice.

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“…Similar expressions will hold for any direction β A = f (β F ) along which the continuum limit β F → ∞ is taken. 18 At T > 0 one can simply substitute L 2 → L s · L t in Eqs. (18,19,22,23).…”

Section: A D =mentioning

confidence: 99%

“…Among these center vortices [12][13][14] have enjoyed broad attention, in particular in the lattice literature. Although most of the effort was put in dealing with gauge fixed schemes, 1 some investigations actually attempted to tackle the problem in a gauge invariant way [17][18][19][20][21][22][23] and are therefore directly related to 't Hooft's original idea.…”

Section: Introductionmentioning

confidence: 99%

Topological order and the vacuum of Yang-Mills theories

Burgio

Reinhardt

2015

Phys. Rev. D

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We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${{z}}$. We show that: i) well defined topological sectors classified by $\pi_1(SO(3))=\mathbb{Z}_2$ can only exist in the ordered phase of ${{z}}$; ii) depending on the dimension $2 \leq d\leq 4$ and action chosen, the center flux exhibits a critical behaviour sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; iii) such critical behaviour does not depend on the temperature $T$. Yang-Mills theories can thus exist in two different continuum phases, characterized by an either topologically ordered or disordered vacuum; this reminds of a quantum phase transition, albeit controlled by the choice of symmetries and not by a physical parameter.Comment: 32 pages, 15 figures. Typos corrected; to appear on PR

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Vortices and confinement in hot and cold D = 2+1 gauge theories

Cited by 20 publications

References 6 publications

Confining strings inSU(N)gauge theories

Confining strings inSU(N)gauge theories

Coulomb versus physical string tension on the lattice

Topological order and the vacuum of Yang-Mills theories

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