Derivation of an Abelian effective model for instanton chains in 3D Yang-Mills theory

Lemos, A. L. L. de; Oxman, L. E.; Teixeira, Bruno Ferreira

doi:10.1103/physrevd.85.125014

Cited by 11 publications

(18 citation statements)

References 52 publications

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“…In a planar system, thin center vortices are localized on points, so they are created or annihilated by a field operator V(x). The emergence of this order parameter can be clearly seen by applying polymer techniques to center-vortex worldlines [38]. In [39], the center-element average for fundamental quarks, over all possible diluted loops, was initially represented in the form…”

Section: Three Dimensionsmentioning

confidence: 99%

From Center-Vortex Ensembles to the Confining Flux Tube

2021

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In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

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Section: Three Dimensionsmentioning

confidence: 99%

From Center-Vortex Ensembles to the Confining Flux Tube

2021

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“…In Ref. [59], the derivation of a three-dimensional effective field model for chains made it possible to relate the monopole (instanton) component with the ZðNÞ-symmetric terms in the 't Hooft model [3]. Therefore, when center vortices condense, monopoles are essential to drive magnetic ZðNÞ SSB and generate an observable domain wall with N-ality, attached to the quark loop.…”

Section: Introductionmentioning

confidence: 99%

4D ensembles of percolating center vortices and monopole defects: The emergence of flux tubes withN-ality and gluon confinement

Oxman

2018

Phys. Rev. D

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Ensembles of magnetic defects represent quantum variables that have been detected and extensively explored in lattice SUðNÞ pure Yang-Mills theory. They successfully explain many properties of confinement and are strongly believed to capture the (infrared) path-integral measure. In this work, we initially motivate the presence of magnetic non-Abelian degrees of freedom in these ensembles. Next, we consider a simple Gaussian model to account for fluctuations. In this case, both center vortices and monopoles become relevant degrees in Wilson loop averages. These physical inputs are then implemented in an ensemble of percolating center vortices in four dimensions by proposing a measure to compute centerelement averages. The introduction of phenomenological information such as monopole tension, stiffness, and fusion leads to an effective YMH model with adjoint Higgs fields. If monopoles also condense, then the gauge group undergoes SUðNÞ → ZðNÞ SSB. This pattern has been proposed as a strong candidate to describe confinement. In the presence of external quarks, these models are known to be dominated by classical solutions, formed by flux tubes with N-ality as well as by confined dual monopoles (gluons).

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“…To perform the ensemble average, we shall closely follow the calculations given in Refs. [20] and [25], based on polymer techniques developed in Refs. [26] and [27], which are briefly reviewed here.…”

Section: Ensemble Averagementioning

confidence: 99%

“…For a discussion involving the coupled equations for the whole tower of angular momenta, see Refs. [40,45]. Summarizing, keeping the dominant term Q 0 , and using Eq.…”

Section: Ensemble Averagementioning

confidence: 99%

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Effective theory of the D = 3 center vortex ensemble

Oxman

Reinhardt

2018

Eur. Phys. J. C

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By means of lattice calculations, center vortices have been established as the infrared dominant gauge field configurations of Yang-Mills theory. In this work, we investigate an ensemble of center vortices in D = 3 Euclidean space-time dimension where they form closed flux loops. To account for the properties of center vortices detected on the lattice, they are equipped with tension, stiffness and a repulsive contact interaction. The ensemble of oriented center vortices is then mapped onto an effective theory of a complex scalar field with a U(1) symmetry. For a positive tension, small vortex loops are favoured and the Wilson loop displays a perimeter law while for a negative tension, large loops dominate the ensemble. In this case the U(1) symmetry of the effective scalar field theory is spontaneously broken and the Wilson loop shows an area law. To account for the large quantum fluctuations of the corresponding Goldstone modes, we use a lattice representation, which results in an XY model with frustration, for which we also study the Villain approximation.

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Derivation of an Abelian effective model for instanton chains in 3D Yang-Mills theory

Cited by 11 publications

References 52 publications

From Center-Vortex Ensembles to the Confining Flux Tube

From Center-Vortex Ensembles to the Confining Flux Tube

4D ensembles of percolating center vortices and monopole defects: The emergence of flux tubes withN-ality and gluon confinement

Effective theory of the D = 3 center vortex ensemble

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