Quantum fluctuations of multi-instanton solutions

Belavin, A. A.; Fateev, V.A.; Schwarz, Albert; Tyupkin, Yu. S.

doi:10.1016/0370-2693(79)91117-1

Cited by 65 publications

(60 citation statements)

References 4 publications

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“…The monopoles consequently carry fractional topological charge. Hence, the theory on the cylinder uncovers a very pleasing picture of instanton constituents, or instanton partons, that were argued to play an important rôle in confinement of ordinary QCD [19][20][21][22][23]. The fact that an instanton configuration on the cylinder is actually a composite of fundamental monopoles has been the subject of number of earlier works [24][25][26][27][28][29].…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Monopoles, affine algebras and the gluino condensate

Davies

Hollowood

Khoze

2003

Journal of Mathematical Physics

133

306

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We examine the low-energy dynamics of four-dimensional supersymmetric gauge theories and calculate the values of the gluino condensate for all simple gauge groups. By initially compactifying the theory on a cylinder we are able to perform calculations in a controlled weakly-coupled way for small radius. The dominant contributions to the path integral on the cylinder arise from magnetic monopoles which play the role of instanton constituents. We find that the semi-classically generated superpotential of the theory is the affine Toda potential for an associated twisted affine algebra. We determine the supersymmetric vacua and calculate the values of the gluino condensate. The number of supersymmetric vacua is equal to c 2 , the dual Coxeter number, and in each vacuum the monopoles carry a fraction 1/c 2 of topological charge. As the results are independent of the radius of the circle, they are also valid in the strong coupling regime where the theory becomes decompactified. In this way we obtain values for the gluino condensate which for the classical gauge groups agree with previously known "weak coupling instanton" expressions (but not with the "strong coupling instanton" calculations). This detailed agreement provides further evidence in favour of the recently advocated resolution of the the gluino condensate puzzle. We also make explicit predictions for the gluino condensate for the exceptional groups.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Monopoles, affine algebras and the gluino condensate

Davies

Hollowood

Khoze

2003

Journal of Mathematical Physics

133

306

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“…Towards large distances the fit was limited by statistical errors. The obtained values for 11 We thank A. Wipf for suggesting to show the N -dependence of the local Polyakov loop distribution. 12 Our lattice spacing is 0.21 f m provided σ(0) = (440 M eV ) 2 .…”

Section: Are the Filtered Fields Confining?mentioning

confidence: 91%

“…Furthermore, calorons contain (gauge independent) magnetic monopoles, see Fig. 1 (a), which realize the scenario of fractional charge objects (also called instanton quarks [11]). For recent progress on calorons, both in the continuum and on the lattice, see [12].…”

Section: Introductionmentioning

confidence: 99%

Laplacian modes probing gauge fields

Bruckmann

Ilgenfritz

2005

Phys. Rev. D

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We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU (2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison.In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.

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“…More generally, the charge 1 SU (N ) caloron 'dissociates' into N constituent monopoles. Hence the caloron realises the old idea of 'instanton quarks' [23] of fractional charge. The lengthes of the intervals on the dual circle give the monopole masses as 8π 2 ν i /β, ν i ≡ µ i+1 −µ i , which upon integration over x 0 make up the unit action of an instanton.…”

Section: Nahm Picture and Substructurementioning

confidence: 99%

Topological objects in QCD

Bruckmann

2007

Eur. Phys. J. Spec. Top.

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Abstract. Topological excitations are prominent candidates for explaining nonperturbative effects in QCD like confinement. In these lectures, I cover both formal treatments and applications of topological objects. The typical phenomena like BPS bounds, topology, the semiclassical approximation and chiral fermions are introduced by virtue of kinks. Then I proceed in higher dimensions with magnetic monopoles and instantons and special emphasis on calorons. Analytical aspects are discussed and an overview over models based on these objects as well as lattice results is given. AppetiserWhen a lattice gauge configuration is subject to cooling, the result can be as depicted in Fig. 1. Without going into details here, this figure reveals typical aspects of a soliton stabilised by topology. In this lecture I will introduce definitions and properties of these beautiful objects and discuss their relevance for particle physics. Before I come to gauge objects like monopoles and instantons, I will demonstrate the main features by virtue of an example in a scalar theory. The kinkAs the first model let us take one of the simplest quantum field theoretical systems, a real scalar field φ in a 1+1 dimensional Minkowski space with metric η µν = diag(+1, −1). The Lagrangian,shall contain a potential V (φ) that has several minima of same height, set to V = 0. For definiteness I will choose the famous mexican hat potential ,a

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Quantum fluctuations of multi-instanton solutions

Cited by 65 publications

References 4 publications

Monopoles, affine algebras and the gluino condensate

Monopoles, affine algebras and the gluino condensate

Laplacian modes probing gauge fields

Topological objects in QCD

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