non-Abelian Fields Research Articles

β-function for topologically massive gluons

We calculate the quantum corrections to the two-point function of four-dimensional topologically massive non-Abelian vector fields at one-loop order for $SU(N)$ gauge theory in Feynman--'t Hooft gauge. We calculate the beta function of the gauge coupling constant and find that the theory becomes asymptotically free faster than pure $SU(N)$ gauge theory.

Non-Abelian Tensor Multiplet Equations from Twistor Space

We establish a Penrose–Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly \({\mathcal{N} = (1, 0)}\) and \({\mathcal{N} = (2, 0)}\) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings.

Numerical study of the Yang-Mills vacuum wave functional inD=3+1dimensions

Ratios of the true Yang-Mills vacuum wave functional, evaluated on any two field configurations out of a finite set of configurations, can be obtained from lattice Monte Carlo simulations. The method was applied some years ago to test various proposals for the vacuum wave functional in $2+1$ dimensions. In this article we use the same method to test our own proposal for the Yang-Mills ground state in $3+1$ dimensions, using two different types of test configurations: Abelian plane waves and non-Abelian constant field configurations. Our proposed vacuum state has the property of ``dimensional reduction'' at large scales, meaning that the (squared) vacuum state, evaluated on long-wavelength, large scale fluctuations, has the form of the Boltzmann weight for Yang-Mills theory in $D=3$ Euclidean dimensions. Our numerical results support this conjectured behavior. We also investigate the form of the ground state evaluated on shorter wavelength configurations.

Pair Production in Non-Perturbative QCD

In this note, we present a method to calculate the vacuum to vacuum transition amplitude in the presence of the non-abelian background field. The number of non-perturbative quark-antiquark produced per unit time, per unit volume and per unit transverse momentum from a given constant chromo-electric field is calculated and compared with the results found in the literature.

Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory

We study a 'composite' or 'dressed' quark in strongly-coupled = 4 super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a Lorentz covariant formula for its rate of radiation.

Non-Abelian color fields from relativistic color charge configurations in the classical limit

We study the dynamics of color fields as generated by simple configurations of relativistic particles with Abelian and non-Abelian [SU(2)] charges in the classical limit. We find that chromodynamic (non-Abelian) systems generally show Coulomb-like features by analogy with electrodynamics. A peculiar feature in the non-Abelian case is the additional strength of the chromoelectric and chromomagnetic fields caused by the contribution of changing the color charge. This change of color SU(2) charges results in a rotation of the color vector, which is getting very fast at close partonic distances. The presence of this non-Abelian additional term in the chromoelectric and chromomagnetic fields creates a color charge glow, which is manifested as a distinct color wave disturbance arising due to the finite distance at which the color interaction becomes active. This situation may be relevant to the hadronization phase in ultrarelativistic heavy-ion collisions, where the partonic state is governed by strong local color fluctuations.

Non-Abelian fields in very special relativity

We study non-Abelian fields in the context of very special relativity (VSR). For this, we define the covariant derivative and the gauge field gauge transformations, both of them involving a fixed null vector ${n}_{\ensuremath{\mu}}$, related to the VSR breaking of the Lorentz group to the Hom(2) or Sim(2) subgroups. As in the Abelian case, the gauge field becomes massive. Moreover, we show that the VSR gauge transformations form a closed algebra. We then write actions coupling the gauge field to various matter fields (bosonic and fermionic). We mention how we can use the spontaneous symmetry-breaking mechanism to give a flavor-dependent VSR mass to the gauge bosons. Finally, we quantize the model using the Becchi-Rouet-Stora-Tyutin formalism to fix the gauge. The model is renormalizable and unitary and for non-Abelian groups, asymptotically free.

The effective field theory of (2 + 1)-dimensional topological insulator in the presence of Rashba spin–orbit interaction

(2 + 1)-dimensional topological insulator described by the Kane–Mele model in the presence of Rashba spin–orbit interaction is considered. The effective action of the external fields coupled to electromagnetic and spin degrees of freedom is accomplished within this model. The Hamiltonian methods are adopted to provide the coefficients appearing in the action. It is demonstrated straightforwardly that the coefficients of the Chern–Simons terms are given by the first Chern number attained through the related non-Abelian Berry gauge field. The effective theory which we obtain is in accord with the existence of the spin Hall phase where the value of the spin Hall conductivity is very close to the quantized one.

A non-abelian vortex lattice in strongly coupled systems

The AdS/CFT correspondence predicts that background non-abelian magnetic fields induce instabilities in strongly-coupled systems with non-abelian global symmetries. These instabilities lead to the formation of vortex lattices in which the non-abelian currents "antiscreen" the applied magnetic field. From the bulk perspective, this behaviour can be traced to a well-known instability of Yang-Mills theory. We analyse the phase structure of the instability and comment on aspects of the vortex lattice.

On the non-abelian global class field theory

Let \(K\) be a global field. The aim of this speculative paper is to discuss the possibility of constructing the non-abelian version of global class field theory of \(K\) by “glueing” the non-abelian local class field theories of \(K_\nu \) in the sense of Koch, for each \(\nu \in \mathbb{h }_K\), following Chevalley’s philosophy of ideles, and further discuss the relationship of this theory with the global reciprocity principle of Langlands.

Gauge dynamics and topological insulators

A non-abelian magnetic field in Yang-Mills theory induces the formation of a "W-boson" vortex lattice. We study the propagation of fundamental fermions in the presence of this lattice in 2+1 dimensions. We show that the spectrum for massless fermions contains four topologically-protected Dirac points with non-zero Bloch momentum. For massive fermions, we compute topological invariants of the band structure and show that it is possible to realise a Z2 topological insulator within Yang-Mills theory.

Electric charge catalysis by magnetic fields and a nontrivial holonomy

We describe a generic mechanism by which a system of Dirac fermions in thermal equilibrium acquires electric charge in an external magnetic field. To this end the fermions should have an additional quantum number, isospin, or color and should be subject to a second magnetic field, which distinguishes the isospin or color, as well as to a corresponding isospin chemical potential. The role of the latter can be also played by a nontrivial holonomy (Polyakov loop) along the Euclidean time direction. The charge is accumulated since the degeneracies of occupied lowest Landau levels for particles of positive isospin and antiparticles of negative isospin are different. We discuss two physical systems where this phenomenon can be realized. One is monolayer graphene, where the isospin is associated with two valleys in the Brillouin zone, and the strain-induced pseudomagnetic field acts differently on charge carriers in different valleys. Another is hot QCD, for which the relevant non-Abelian field configurations with both nonzero chromomagnetic field and a nontrivial Polyakov loop can be realized as calorons---topological solutions of Yang-Mills equations at finite temperature. The induced electric charge on the caloron field configuration is studied numerically. We argue that due to the fluctuations of holonomy, the external magnetic field should tend to suppress charge fluctuations in the quark-gluon plasma and estimate the importance of this effect for off-central heavy-ion collisions.

Duality-symmetric actions for non-Abelian tensor fields

We construct the duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to one another by first-order (self-)duality equations that follow from these actions. In particular, this construction provides a Lorentz invariant action for non-Abelian self-dual tensor fields. The class of models includes the bosonic sectors of the $6d$ (1,0) superconformal models of interacting non-Abelian self-dual tensor, vector, and hypermultiplets.

Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.

Neutrino oscillations in Stueckelberg semiclassical relativistic dynamics

The Stueckelberg formulation of a manifestly covariant relativistic classical and quantum mechanics is briefly reviewed and it is shown that in this framework a simple (semiclassical) model exists for the description of neutrino oscillations. The model is shown to be consistent with the field equations and the Lorentz force (developed here without and with spin by canonical methods) for Glashow-Salam-Weinberg type non-Abelian fields interacting with the leptons. We discuss a possible fundamental mechanism, in the context of a relativistic theory of spin for (first quantized) quantum mechanical systems, for CP violation. The model also predicts a possibly small "pull back,", i.e., early arrival of a neutrino beam, for which the neutrino motion is almost everywhere within the light cone, a result which may emerge from future long baseline experiments designed to investigate neutrino transit times with significantly higher accuracy than presently available.

Strong-field physics as a new probe of early-time dynamics in heavy-ion collisions

In high-energy heavy-ion collisions, there appear two kinds of extremely strong fields: Ordinary electromagnetic fields and non-Abelian color Yang-Mills fields called a glasma. I explain how they are created in collisions, how strong they are, and how important they are in understanding early-time "pre-equilibrium" evolution of collision events. As one of the typical strong-field "nonlinear QED" phenomena, I discuss possible relevance of the "vacuum birefringence" of a photon in probing the very early-time dynamics of heavy-ion collisions.

Isotropy theorem for cosmological Yang-Mills theories

We consider homogeneous non-abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills fields is always isotropic and has the perfect fluid form for any locally inertial observer.

Localization of matter fields and non-Abelian gauge fields on domain walls

We propose a method for simultaneous localization of non-Abelian gauge fields and matter fields with minimal interaction on domain walls using U(N)c gauge theory with SU(N)L × SU(N)R × U(1)A flavor symmetry. Localization of non-Abelian fields is achieved using field-dependent gauge coupling. We find that effective Lagrangian up to second order of derivatives for low energy fluctuations resembles a chiral model from hadron physics with additional minimal interactions of pions with localized gauge fields together with nonlinear interactions of moduli fields. This result provides a step towards a realistic model building of brane-world scenario using topological solitons.

Physical unitarity for a massive Yang-Mills theory without the Higgs field: A perturbative treatment

In a series of papers, we examine the physical unitarity in a massive Yang-Mills theory without the Higgs field in which the color gauge symmetry is not spontaneously broken and kept intact. For this purpose, we use a new framework proposed in the previous paper Kondo [arXiv:1208.3521] based on a nonperturbative construction of a non-Abelian field describing a massive spin-one vector boson field, which enables us to perform the perturbative and nonperturbative studies on the physical unitarity. In this paper, we present a new perturbative treatment for the physical unitarity after giving the general properties of the massive Yang-Mills theory. Then we reproduce the violation of physical unitarity in a transparent way. This paper is a preliminary work to the subsequent papers in which we present a nonperturbative framework to propose a possible scenario of restoring the physical unitarity in the Curci-Ferrari model.

Nonperturbative construction of massive Yang-Mills fields without the Higgs field

In order to understand the so-called decoupling solution for gluon and ghost propagators in QCD, we give a nonperturbative construction of a massive vector field describing a non-Abelian massive spin-one particle, which has the correct physical degrees of freedom and is invariant under a modified Becchi-Rouet-Stora-Tyutin transformation, in a massive Yang-Mills model without the Higgs field, i.e., the Curci-Ferrari model. The resulting non-Abelian massive vector boson field is written using a nonlinear but local transformation from the original fields in the Curci-Ferrari model. As an application, we write down a local mass term for the Yang-Mills field and a dimension-two condensate, which are exactly invariant under the modified Becchi-Rouet-Stora-Tyutin transformation, Lorentz transformation and color rotation.