Instantons in the Maximally Abelian gauge

Brower, Richard C.; Orginos, Konstantinos; Tan, C-I

doi:10.1016/s0920-5632(96)00695-0

Cited by 8 publications

(7 citation statements)

References 2 publications

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“…So in this special configuration the exponent is proportional to σ 3 and the path ordering becomes trivial, as in the abelian theory. More generally, it should always be possible to choose a gauge in which the connection along a given curve is a non-vanishing constant (analogous comments concerning the maximally abelian gauge appear in [19,20,21]). The integration over the angle φ followed by evaluation of the trace leads to (dropping the subscript 0)…”

Section: The Wilson Loop In the Bosonic Modelmentioning

confidence: 99%

Instanton corrections to circular Wilson loops in Script N = 4 Supersymmetric Yang-Mills

Bianchi¹,

Green²,

Kovacs³

2002

J. High Energy Phys.

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It is argued that whereas supersymmetry requires the instanton contribution to the expectation value of a straight Wilson line in the N = 4 supersymmetric SU (2) Yang-Mills theory to vanish, it is not required to vanish in the case of a circular Wilson loop. A non-vanishing value can arise from a subtle interplay between a divergent integral over bosonic moduli and a vanishing integral over fermionic moduli. The one-instanton contribution to such Wilson loops is explicitly evaluated in semi-classical approximation. The method utilizes the symmetries of the problem to perform the integration over the bosonic and fermionic collective coordinates of the instanton. The integral is singular for small instantons touching the loop and is regularized by introducing a cutoff at the boundary of the (euclidean) AdS 5 moduli space. In the case of a circular loop a nonzero finite result is obtained when the cutoff is removed and a perimeter divergence subtracted. This is contrasted with the case of the straight line where the result is zero after subtraction of an identical divergence per unit length. The linear divergence is an artifact of our non supersymmetric regulator that deserves further consideration. The generalization to gauge group SU (N ) with arbitrary N is straightforward in the limit of small 't Hooft coupling. The extension to strong 't Hooft coupling is more challenging and only a qualitative discussion is given of the AdS/CFT correspondence.

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Section: The Wilson Loop In the Bosonic Modelmentioning

confidence: 99%

Instanton corrections to circular Wilson loops in Script N = 4 Supersymmetric Yang-Mills

Bianchi¹,

Green²,

Kovacs³

2002

J. High Energy Phys.

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“…The instanton is another relevant topological object in QCD according to Π 3 (SU(N c )) =Z ∞ . Recent studies reveal close relation between instantons and QCD-monopoles [6,8,[13][14][15]18,19].…”

Section: Instantons and Qcd-monopolesmentioning

confidence: 99%

“…µ ] MA ≃ 0 after several cooling. Hence, instantons can be regarded as 'seeds' of QCD-monopoles [6,8,10,13,14,18,19].…”

Section: Instantons and Qcd-monopolesmentioning

confidence: 99%

Instanton, monopole condensation and confinement

Suganuma

Fukushima

Ichie

et al. 1998

Nuclear Physics B - Proceedings Supplements

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The confinement mechanism in the nonperturbative QCD is studied in terms of topological excitation as QCDmonopoles and instantons. In the 't Hooft abelian gauge, QCD is reduced into an abelian gauge theory with monopoles, and the QCD vacuum can be regarded as the dual superconductor with monopole condensation, which leads to the dual Higgs mechanism. The monopole-current theory extracted from QCD is found to have essential features of confinement. We find also close relation between monopoles and instantons using the lattice QCD. In this framework, the lowest 0 ++ glueball (1.5 ∼ 1.7GeV) can be identified as the QCD-monopole or the dual Higgs particle. Dual Higgs Theory for NP-QCDQuantum chromodynamics (QCD) is established as the strong-interaction sector in the Standard Model, and the perturbative QCD provides the powerful and systematic method in analyzing high-energy experimental data. However, QCD is a 'black box' in the infrared region still now owing to the strong-coupling nature, although there appear rich phenomena as color confinement, dynamical chiral-symmetry breaking and topological excitation in the nonperturbative QCD (NP-QCD). In particular, confinement is the most outstanding feature in NP-QCD, and to understand the confinement mechanism is a central issue in hadron physics.In 1974, Nambu [1] presented an interesting idea that quark confinement and string picture for hadrons can be interpreted as the squeezing of the color-electric flux by the dual Meissner effect, which is similar to formation of the Abrikosov vortex in the type-II superconductor. This dual superconductor picture for the NP-QCD vacuum is based on the duality in the Maxwell equation, and needs condensation of color-magnetic monopoles, which is the dual version of electriccharge (Cooper-pair) condensation in the superconductivity.In 1981, 't Hooft [2] pointed out that colormagnetic monopoles appear in QCD as topological excitation in the abelian gauge [2,3], which diagonalizes a gauge-dependent variable X(s).Here, SU(N c ) gauge degrees of freedom is partially fixed except for the maximal torus subgroup U(1) Nc−1 and the Weyl group. In the abelian gauge, QCD is reduced into a U(1) Nc−1gauge theory, and monopoles with unit magnetic charge appear at hedgehog-like configurations according to the nontrivial homotopy group,In 90's, the Monte Carlo simulation based on the lattice QCD becomes a powerful tool for the analysis of the confinement mechanism using the maximally abelian (MA) gauge [7][8][9][10][11][12][13][14][15], which is a special abelian gauge minimizing the off-diagonal components of the gluon field. Recent lattice studies with MA gauge have indicated monopole condensation in the NP-QCD vacuum [7-9] and the relevant role of abelian degrees of freedom, abelian dominance [9-12], for NP-QCD. In the lattice QCD in MA gauge, monopole dominance for NP-QCD is also observed as the essential role of QCD-monopoles for the linear quark potential [10], chiral symmetry breaking [11,12] and instantons [6,13,14].In this paper, we study Q...

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“…4, consists of the straight line monopole trajectory which goes through the center of the instanton. A more complicated solution [35], shown in Fig. 5, consists of the circular monopole current of radius R, and the instanton of the width ρ at the center of the monopole trajectory.…”

Section: Monopoles and Instantonsmentioning

confidence: 99%