Magnetic monopole dynamics, supersymmetry, and duality

Weinberg, Erick J.; Yi, Piljin

doi:10.1016/j.physrep.2006.11.002

Cited by 147 publications

(213 citation statements)

References 297 publications

(749 reference statements)

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“…For the monopole in the G 2 case and the quantization of the magnetic charges, please see [34][35][36] and [37][38][39].…”

Section: Jhep02(2018)158mentioning

confidence: 99%

Low-energy dynamics of 3d N $$ \mathcal{N} $$ = 2 G2 supersymmetric gauge theory

Nii

Sekiguchi

2018

J. High Energ. Phys.

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We study a three-dimensional N = 2 supersymmetric G 2 gauge theory with and without fundamental matters. We find that a classical Coulomb branch of the moduli space of vacua is partly lifted by monopole-instantons and the quantum Coulomb moduli space would be described by a complex one-dimensional space. Depending on the number of the matters in a fundamental representation, the low-energy dynamics of the theory shows various phases like s-confinement or quantum merging of the Coulomb and the Higgs branches. We also investigate superconformal indices as an independent check of our analysis.

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“…For the monopole in the G 2 case and the quantization of the magnetic charges, please see [34][35][36] and [37][38][39].…”

Section: Jhep02(2018)158mentioning

confidence: 99%

Low-energy dynamics of 3d N $$ \mathcal{N} $$ = 2 G2 supersymmetric gauge theory

Nii

Sekiguchi

2018

J. High Energ. Phys.

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“…is decomposed into two pieces V µ (x) and X µ (x): 12) such that the first piece V µ (x) transforms with the inhomogeneous term under the gauge transformation U(x) ∈ G: 13) in the same way as the original Yang-Mills field:…”

Section: Decomposing the Su(2) Yang-mills Fieldmentioning

confidence: 99%

“…Suppose that the color direction at each point of space-time is specified by a field n(x) = {n A (x)} in d = dimG dimensional color space for the gauge group G: We prepare initially a color field n: 12) where its magnitude is fixed as…”

Section: General Considerationmentioning

confidence: 99%

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Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the YangMills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator.Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gaugeinvariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations.However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability 1 groupH of G, while there is a unique option ofH = U(1) for G = SU(2). The maximal stability group depends...

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“…Here we check the steps in the verification of the Nahm construction, following closely the steps in [8]. We make the ansatz…”

Section: B Verifying the Adhmn Construction In Loop Spacementioning

confidence: 99%

Selfdual strings and loop space Nahm equations

Gustavsson¹

2008

J. High Energy Phys.

244

274

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We give two independent arguments why the classical membrane fields should be take values in a loop algebra. The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations. The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as su(N ) for any N ) that satisfies the algebraic structure of the membrane theory.

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Magnetic monopole dynamics, supersymmetry, and duality

Cited by 147 publications

References 297 publications

Low-energy dynamics of 3d N $$ \mathcal{N} $$ = 2 G2 supersymmetric gauge theory

Low-energy dynamics of 3d N $$ \mathcal{N} $$ = 2 G2 supersymmetric gauge theory

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

Selfdual strings and loop space Nahm equations

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