Monopoles, Vortices and Strings: Confinement and Deconfinement in 2+1 Dimensions at Weak Coupling

Kogan, Ian I.; Kovner, Alex

doi:10.1142/9789812777270_0003

Cited by 15 publications

(28 citation statements)

References 43 publications

(97 reference statements)

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“…By using the change of variables r = x KK − x BPS , and then going to spherical coordinates, the integral I B (defined below) over the bion constituent collective coordinates becomes: 33) with the effective potential: 34) and: 35) while V is the 3-space volume 12 and r min ∼ 1/L denotes the fact that we are working in a dilute gas approximation and in the effective long-distance field theory, hence the BPS and KK monopoles can not be "on top" of each other.…”

Section: Computation Of Z Bionmentioning

confidence: 99%

Microscopic structure of magnetic bions

Anber

Poppitz

2011

J. High Energ. Phys.

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Abstract:Magnetic bions-stable bound states of monopoles and twisted ("Kaluza-Klein") monopoles, carrying two units of magnetic charge-have been shown to be the leading cause of confinement and mass gap in four-dimensional gauge theories with massless adjoint fermions compactified on R 1,2 × S 1 , at least at small S 1 . In this paper, we study in detail the bion mechanism and the scales involved for an SU (2) gauge group, using traditional QCD instanton methods. We represent the vacuum functional as the partition function of a bion-anti-bion plasma and obtain the next-to-leading dependence of the mass gap on the S 1 size L at fixed strong-coupling scale Λ. We find that, at small ΛL, the mass gap is an increasing function of L for theories with four massless adjoint Weyl fermions, a case left undetermined by the previous leading-order analysis, and comment on the approach to R

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Section: Computation Of Z Bionmentioning

confidence: 99%

Microscopic structure of magnetic bions

Anber

Poppitz

2011

J. High Energ. Phys.

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“…Many-body treatment is a powerful tool in condensed matter systems. In the present work, we adapt this method to take into account the effect of monopole-instantons which, to the best of our 4 Also see [18,19] for reviews.…”

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confidence: 99%

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

Anber

2014

Annals of Physics

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Abstract:The confinement problem remains one of the most difficult problems in theoretical physics. An important step toward the solution of this problem is the 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 Wbosons 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 monopoleinstantons as external background field. Using this construction, we calculate the exact 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 < M W , where M W 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 twocomponent 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.

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“…Nevertheless we may expect (Refs. [2], [4]- [13]) that topological configurations are relevant for the infrared behaviour of the theory. The first question is whether the configurations (2.2) have any topological significance.…”

Section: Yang-mills Theory and Monopolesmentioning

confidence: 99%

Integrating topological degrees of freedom with perturbation theory in three dimensional Yang-Mills theory

Chatterjee¹

2012

Proceedings of Sixth International Conference on Quarks and Nuclear Physics — PoS(QNP2012)

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Polyakov has demonstrated that a monopole plasma gives confinement in Georgi Glashow model in three Euclidean dimensions. However his semi classical techniques are not applicable for pure YM 3 . Even though the gauge potential ansatz of 't Hooft Polyakov monopole has a finite action in YM 3 , it is not a stable classical solution, indeed, larger the 'size' smaller the action. We develop techniques for summing over such large overlapping monopole configurations. This is based on i) characterizing the configurations using eigenfunctions of B i (x) · B j (x), ii) obtaining a two potential formalism for Yang Mills theory. These techniques provide a way for combining renormalized perturbation theory and asymptotic freedom with confining effects of fluctuations of topological significance.

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Monopoles, Vortices and Strings: Confinement and Deconfinement in 2+1 Dimensions at Weak Coupling

Cited by 15 publications

References 43 publications

Microscopic structure of magnetic bions

Microscopic structure of magnetic bions

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

Integrating topological degrees of freedom with perturbation theory in three dimensional Yang-Mills theory

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