Nielsen-Olesen Instability Research Articles

Magnetic field and curvature effects on pair production. II. Vectors and implications for chromodynamics

We calculate the pair production rates for spin-$1$ or vector particles on spaces of the form $M \times {\mathbb R}^{1,1}$ with $M$ corresponding to ${\mathbb R}^2$ (flat), $S^2$ (positive curvature) and $H^2$ (negative curvature), with and without a background (chromo)magnetic field on $M$. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for $S^2$ and $H^2$ is obtained. We also give a brief discussion of how our results relate to ideas about confinement in nonabelian theories.

Parametric instability of classical Yang-Mills fields in a color magnetic background

We investigate instabilities of classical Yang-Mills fields in a time-dependent spatially homogeneous color magnetic background field in a non-expanding geometry for elucidating the earliest stage dynamics of ultra-relativistic heavy-ion collisions. The background gauge field configuration considered in this article is spatially homogeneous and temporally periodic, and is alluded by Berges-Scheffler-Schlichting-Sexty (BSSS). We discuss the whole structure of instability bands of fluctuations around the BSSS background gauge field on the basis of Floquet theory, which enables us to discuss the stability in a systematic way. We find various instability bands on the $(p_z, p_T)$-plane. These instability bands are caused by parametric resonance despite the fact that the momentum dependence of the growth rate for $|\mathbf{p}| \leq \sqrt{B}$ is similar to a Nielsen-Olesen instability. Moreover, some of instability bands are found to emerge not only in the low momentum but also in the high momentum region; typically of the order of the saturation momentum as $|\mathbf{p}| \sim \sqrt{B} \sim Q_{\rm s}$.

Stability of chromomagnetic condensation and mass generation for confinement in SU(2) Yang-Mills theory

We show that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous chromomagnetic condensation disappears in the framework of the functional renormalization group. This result follows from our observations: (i) the vanishing imaginary part of the effective average action is realized for arbitrary infrared cutoff as a novel fixed point solution of the flow equation for the complex-valued effective average action and (ii) an approximate analytical solution for the effective average action is obtained without the pure imaginary part for large infrared cutoff. This result suggests that there exists a physical mechanism for maintaining the stability or staying on the fixed point even for sufficiently small infrared cutoff. We argue that dynamical gluon mass generation (related to two-gluon bound states identified with glueballs) occurs due to the Becchi-Rouet-Stora-Tyutin-invariant vacuum condensate of mass dimension two without causing instability.

Schwinger mechanism enhanced by the Nielsen–Olesen instability

We discuss gluon production by the Schwinger mechanism in collinear color-electric and magnetic fields which may be realized in pre-equilibrium stages of ultra-relativistic heavy-ion collisions. Fluctuations of non-Abelian gauge fields around a purely color-magnetic field contain exponentially growing unstable modes in a longitudinally soft momentum region, which is known as the Nielsen–Olesen instability. With a color-electric field imposed parallelly to the color-magnetic field, we can formulate this instability as the Schwinger mechanism. This is because soft unstable modes are accelerated by the electric fields to escape from the instability condition. Effects of instability remain in the transverse spectrum of particle modes, leading to an anomalously intense Schwinger particle production.

Out-of-equilibrium dynamics of coherent non-Abelian gauge fields

We study out-of-equilibrium dynamics of intense non-Abelian gauge fields. Generalizing the well-known Nielsen-Olesen instabilities for constant initial color-magnetic fields, we investigate the impact of temporal modulations and fluctuations in the initial conditions. This leads to a remarkable coexistence of the original Nielsen-Olesen instability and the subdominant phenomenon of parametric resonance. Taking into account that the fields may be correlated only over a limited transverse size, we model characteristic aspects of the dynamics of color flux tubes relevant in the context of heavy-ion collisions.

Instabilities in non-expanding glasma

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.

Decay of Color Gauge Fields in Heavy Ion Collisions and Nielsen-Olesen Instability

We analyze the behavior of unstable modes in the glasma produced in high-energy heavyion collisions, using a simple model with effective homogeneous longitudinal color electric and magnetic fields. The unstable modes are approximately described as Nielsen-Olesen unstable modes under the homogeneous longitudinal gauge fields. We find that the Nielsen-Olesen unstable modes show properties very similar to those of the exponentially increasing unstable modes in the glasma recently demonstrated by Romatschke and Venugopalan. Although initial gauge fields in the glasma are much stronger than those in our model, they decay with the production of Nielsen-Olesen unstable modes. We discuss why we can reproduce the features of the glasma effectively by using homogeneous weak magnetic fields. Our analysis supports the idea that the decay of the gauge fields in the glasma is caused by Nielsen-Olesen instability.

Resolving the instability of the Savvidy vacuum by dynamical gluon mass

In this Letter we apply the formalism of local composite operators as developed by Verschelde et al. in combination with a constant chromomagnetic field as considered in the seventies by Savvidy and others. We find that a nonzero 〈Aμ2〉 minimizes the vacuum energy, as in the case with no chromomagnetic field, and that the chromomagnetic field itself is near-to zero. The Nielsen–Olesen instability, caused by the imaginary part in the action, also vanishes. We further investigate the effect of an external chromomagnetic field on the value of 〈Aμ2〉, finding that this condensate is destroyed by sufficiently strong fields. The inverse scenario, where 〈Aμ2〉 is considered as external, results in analogous findings: when this condensate is sufficiently large, the induced chromomagnetic field is lowered to a perturbative value slightly below the applied 〈Aμ2〉.

Thermalization of Color Gauge Fields in Heavy Ion Collisions and Nielsen-Olesen Instability

We analyze the behavior of unstable modes in glasma produced initially in high energy heavy ion collisions, by using a simple model of homogeneous longitudinal color electric and magnetic fields. The unstable modes can be approximately described as Nielsen-Olesen unstable modes under the homogeneous longitudinal gauge fields. We find that the NielsenOlesen unstable modes show properties very similar to those of the exponentially increasing unstable modes in glasma demonstrated recently by Romatschke and Venugopalan. We discuss why such effective weak magnetic fields used in the model are appropriate to analyze the instability of the initial strong inhomogeneous gauge fields. Our analysis indicates that the decay of the gauge fields in glasma is caused by not Weibel instability but Nielsen-Olesen instability.

Phenomenology of symmetry breaking from extra dimensions

Motivated by the electroweak hierarchy problem, we consider theories with two extra dimensions in which the four-dimensional scalar fields are components of gauge boson in full space. We explore the Nielsen-Olesen instability for SU(N) on a torus, in the presence of a magnetic background. A field theory approach is developed, computing explicitly the minimum of the complete effective potential, including tri-linear and quartic couplings and determining the symmetries of the stable vacua. We also develop appropriate gauge-fixing terms when both Kaluza-Klein and Landau levels are present and interacting, discussing the interplay between the possible six and four dimensional choices. The equivalence between coordinate dependent and constant Scherk-Schwarz boundary conditions -associated to either continuous or discrete Wilson lines- is analyzed.

Unstable magnetic fluxes in heterotic string theory

We study exact string backgrounds representing a constant magnetic field background in heterotic string theory. These backgrounds are obtained by Kaluza-Klein reduction of a special class of plane wave solutions. For small values of the magnetic field they possess localized closed string tachyons analogous to the Nielsen-Olesen instability of a constant magnetic field in SO(3) Yang-Mills theory. When the magnetic field is embedded in the SO(32) gauge group of the heterotic string it is possible to study the lowest level tachyon in supergravity. We identify the closed string tachyons as fluctuations of the supergravity fields about the background. We argue that the tachyon signals the decay of the background to flat space. Our evidence rests on the study of the closed string tachyon potential, world sheet renormalization group equations in the supergravity approximation and the S-dual of this system in type I theory. In the S-dual description, the closed string tachyons in heterotic string theory correspond to open string tachyons in type I theory. Finally we analyze the non-perturbative stability of these models representing constant magnetic field backgrounds and show that it is stable to pair production of particles.

Stability of quark gluon plasma to nielsen-olesen mode

Nielsen and Olesen showed that perturbative vacuum with uniform chromomagnetic field in one space and one color direction is unstable. This instability is called Nielsen-Olesen instability (NOI), and leads to formation of a ‘spaghetti of flux tubes’ as a model for non-perturbative vacuum and confinement. We re-examine this instability in presence of color sources, quarks and gluons, at a finite temperature and find that at sufficiently high temperature NOI is stabilized due to an ‘effective mass’ of gluons arising through plasma effects. This explains how a QGP with no confinement effects may exist at high temperature. As the temperature is lowered, NOI reappears at a valueT=Tc, which is very close to confinement-deconfinement transition from hadrons to QGP..