An unstable Yang-Mills field mode

Nielsen, N.K.; Olesen, P.

doi:10.1016/0550-3213(78)90377-2

Cited by 669 publications

(607 citation statements)

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“…For technical reasons, we formulate everything in the Abelian decomposed representation as in the original presentation by Nielsen and Olesen [5]. We then discuss the consequences of this N-O instability.…”

Section: The N-o Instability and Induced Currentmentioning

confidence: 99%

“…It has been well known that the configuration of a homogeneous magnetic field in non-Abelian gauge theories exhibits instability with respect to fluctuations perpendicular to the magnetic field in the color space. This is called the Nielsen-Olesen (N-O) instability [5]. This can be most easily understood when we recast the theory in terms of the U(1) "electromagnetic field" A µ ≡ A 3 µ and the "charged vector fields"…”

Section: The N-o Instability In the Abelian Decomposed Representationmentioning

confidence: 99%

“…Preceding studies on this subject [2] include the scenario based on the plasma instability (in particular, the Weibel instability) caused by coupling between hard particles and soft fields [3], the 'bottom-up' scenario based on the perturbative scatterings of hard particles [4], and so on. In addition to them, we have recently proposed a novel scenario based on the Nielsen-Olesen (N-O) instability [5] which is characteristic of the configuration of a uniform magnetic field in non-Abelian gauge theories [6,7]. This scenario applies the earliest time evolution of the system in the heavy ion collision when the separation between hard and soft degrees of freedom is not clear.…”

Section: Introductionmentioning

confidence: 99%

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Instabilities in non-expanding glasma

2009

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A homogeneous color magnetic field is known to be unstable for the fluctuations perpendicular to the field in the color space (the Nielsen-Olesen instability). We argue that these unstable modes, exponentially growing, generate an azimuthal magnetic field with the original field being in the z-direction, which causes the Nielsen-Olesen instability for another type of fluctuations. The growth rate of the latter unstable mode increases with the momentum p z and can become larger than the former's growth rate which decreases with increasing p z . These features may explain the interplay between the primary and secondary instabilities observed in the real-time simulation of a non-expanding glasma, i.e., stochastically generated anisotropic Yang-Mills fields without expansion.

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Section: The N-o Instability and Induced Currentmentioning

confidence: 99%

Section: The N-o Instability In the Abelian Decomposed Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Instabilities in non-expanding glasma

2009

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“…i) Nielsen-Olesen instability [140] of the Savvidy vacuum [139]: the vacuum (in)stability under the uniform chromomagnetic field or stability of the chromomagnetic condensation. See [123,20,124].…”

Section: Integrating Out the Infrared Non-dominant Field X µmentioning

confidence: 99%

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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“…More recently, Bachas [2] analysed the effect of Fradkin-Tseytlin deformations [3,4] on open strings, and showed how their universal magnetic couplings [5] can lead to chiral spectra with broken supersymmetry. However, these models have in general Nielsen-Olesen instabilities [6], that reflect themselves in the emergence of tachyonic modes. This complicates the analysis, and brings about some surprises.…”

mentioning

confidence: 99%

Type-I strings on magnetised orbifolds and brane transmutation

Angelantonj¹,

Antoniadis

Dudas³

et al. 2000

Physics Letters B

311

433

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In the presence of internal magnetic fields, a D9 brane can acquire a D5 (or anti-D5) R-R charge, and can therefore contribute to the corresponding tadpole. In the resulting vacua, supersymmetry is generically broken and tachyonic instabilities are present. However, suitable choices for the magnetic fields, corresponding to selfdual configurations in the internal space, can yield new chiral supersymmetric vacua with gauge groups of reduced rank, where the magnetic energy saturates, partly or fully, the negative tension of the O5 + planes. These models contain Green-Schwarz couplings to untwisted R-R forms not present in conventional orientifolds.

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An unstable Yang-Mills field mode

Cited by 669 publications

References 5 publications

Instabilities in non-expanding glasma

Instabilities in non-expanding glasma

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

Type-I strings on magnetised orbifolds and brane transmutation

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