non-Abelian Fields Research Articles

A general recipe to observe non-Abelian gauge field in metamaterials

Abstract Recent research on non-Abelian phenomena has cast a new perspective on controlling light. In this work, we provide a simple and general approach to induce non-Abelian gauge field to tremble the light beam trajectory. With in-plane duality symmetry relaxed, our theoretical analysis finds that non-Abelian electric field can be synthesized through a simple real-space rotation of any biaxial material. With orthogonal optical modes excited, their interference leads to an oscillation of the propagating optical beam, which is a direct consequence of the emergence of non-Abelian electric field, influencing light in a manner similar with how electric fields act on charged particles. Our microwave experiments provide unambiguous evidence to the observation of such an optical Zitterbewegung effect where excellent agreement can be found between theorical derivation, numerical simulations and experiments. By extending the idea to optical regime using natural material, we here provide another example to shake the general intuition that light travels in straight lines in homogeneous media.

Digital Quantum Simulation of a (1+1)D SU(2) Lattice Gauge Theory with Ion Qudits

We present a quantum simulation strategy for a (1+1)-dimensional SU(2) non-Abelian lattice gauge theory with dynamical matter, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion-qudit quantum processor, as recently experimentally realized [Nat. Phys. 18, 1053 (2022)]. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss’s law. We discuss the experimental feasibility of generalized Mølmer-Sørensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically relevant properties specific to non-Abelian field theories, such as baryon excitations. Published by the American Physical Society 2024

Local Non Abelian Class Field Theory

The “local class field theory”, which can be defined as the description of the extensions of a given local field K in terms of the algebraic and analytic objects depending ony on the base K is one of the central problems of modern number theory. The theory developed for the abelian extensions, around the fundamental works of Artin and Hasse in the first quarter of the 20th century. It is natural to ask if one could construct this theory including the non-abelian extensions of the base field. There are two approches to this problem. One approach is based on the ideas of Langlands, and the other on Koch. Koch’s method was later generalized by Fesenko and Koch-de Shalit for some non-abelian extensions of the base field. On the other hand, Ikeda and Serbest extended Fesenko’s works to construct a non-abelian local class field theory. But there is a restriction for the base field K. In this study, we extended Ikeda-Serbest’s construction of the local reciprocity map for a certain local field to any local field. Also we have shown that the extended map satisfies the certain functoriality and ramification theoretic properties.

Spin-charged point particle in a non-Abelian external field with the generalized uncertainty relation

The dynamics of a particle carrying a non-Abelian charge is studied in the presence of a minimal length. By choosing an appropriate non-Abelian gauge field, the system identifies with the Hamiltonian of the Jaynes-Cummings model whose solutions can be determined algebraically. The model has an underlying graded Lie algebra symmetry reminiscent of supersymmetric quantum mechanics. We calculate the energy levels and associated eigenstates using conservation of the number of excitations of the system. Then, we present the effect of the minimal length on the dynamics of the system and we are particularly interested in two particular cases, that of Rabi oscillations and that of the collapse-revival of the wave function. The results show that the higher the deformation parameter, the faster the oscillatory behavior of the atomic inversion.

Conformal Yang-Mills field in arbitrary dimensions

Lagrangian of a classical conformal Yang-Mills field in the flat space of even dimension greater than or equal to six involves higher derivatives. We study Lagrangian formulation of the classical conformal Yang-Mills field by using ordinary-derivative (second-derivative) approach. In the framework of the ordinary-derivative approach, a field content, in addition to generic Yang-Mills field, consists of auxiliary vector fields and Stueckelberg scalar fields. For such field content, we obtain a gauge invariant Lagrangian with the conventional second-derivative kinetic terms and the corresponding gauge transformations. The Lagrangian is built in terms of non-abelian field strengths. Structure of a gauge algebra entering gauge symmetries of the conformal Yang-Mills field is described. FFF-vertex of the conformal Yang-Mills field which involves three derivatives is also obtained. For six, eight, and ten dimensions, eliminating the auxiliary vector fields and gauging away the Stueckelberg scalar fields, we obtain a higher-derivative Lagrangian of the conformal Yang-Mills field. For arbitrary dimensions, we demonstrate that all auxiliary fields can be integrated out at non-linear level leading just to a local higher-derivative action which is expressed only in terms of the generic Yang-Mills field.

Non-Abelian magnetic field and curvature effects on pair production

Non-Abelian magnetic field and curvature effects on pair production

Regular dessins with moduli fields of the form Q(ζp, \sqrt[p]{q})

Gareth Jones asked during the 2014 SIGMAP conference for examples of regular dessins with nonabelian fields of moduli. In this paper, we first construct dessins whose moduli fields are nonabelian Galois extensions of the form Q(ζp, \sqrt[p]{q}), where p is an odd prime and ζp is a pth root of unity and q ∈ Q is not a pth power, and we then show that their regular closures have the same moduli fields. Finally, in the special case p = q = 3 we give another example of a regular dessin with moduli field Q(ζ3, ∛(3)) of degree 219 · 34 and genus 14155777.

Ferromagnetic phase transitions in SU(N)

We study the thermodynamics of a non-abelian ferromagnet consisting of “atoms” each carrying a fundamental representation of SU(N), coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global SU(N)-invariant states to magnetized ones breaking global invariance to SU(N−1)×U(1). Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual SU(2) ferromagnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model.

Composing arbitrarily many SU(N) fundamentals

We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number n of fundamental representations of SU(N), and we identify a duality in the representation content of this decomposition. Our method utilizes the mapping of the representations of SU(N) to the states of free fermions on the circle, and can be viewed as a random walk on a multidimensional lattice. We also derive the large-n limit and the response of the system to an external non-abelian magnetic field. These results can be used to study the phase properties of non-abelian ferromagnets and to take various scaling limits.

AdS black brane coupled to non-abelian logarithmic gauge theory and color DC conductivity

In this paper, we consider Einstein–Hilbert gravity in the presence of cosmological constant and non-abelian nonlinear electromagnetic field of logarithmic type that is minimally coupled to gravity. First, black brane solution of this model is introduced and then color non-abelian DC conductivity is calculated for this solution by using AdS/conformal field theory (CFT) duality. Our result recovers the Yang–Mills model in λ → 0 limit.

Spin-texture topology in curved circuits driven by spin-orbit interactions

Interferometry is a powerful technique used to extract valuable information about the wave function of a system. In this work, we study the response of spin carriers to the effective field textures developed in curved one-dimensional interferometric circuits subject to the joint action of Rashba and Dresselhaus spin-orbit interactions. By using a quantum network technique, we establish that the interplay between these two non-Abelian fields and the circuit’s geometry modify the geometrical characteristics of the spinors, particularly on square circuits, leading to the localisation of the electronic wave function and the suppression of the quantum conductance. We propose a topological interpretation by classifying the corresponding spin textures in terms of winding numbers.

Flat bands, quantum Hall effect and superconductivity in twisted bilayer graphene at magic angles

Flat band electronic modes are responsible for superconductivity in twisted bilayer graphene (TBG) rotated at magic angles. From there other magic angles can be found for any multilayered twisted graphene systems. Eventually, this lead to the discovery of the highest ever known electron-electron correlated material. Moreover, the quantum phase diagram of TBG is akin to those observed among high-Tc superconductors and thus there is a huge research effort to understand TBG in the hope of clarifying the physics behind such strong correlations. A particularity of the TBG is the coexistence of superconductivity and the fractional Quantum Hall effect, yet this relationship is not understood. In this work, a simple 2 × 2 matrix model for TBG is introduced. It contains the magic angles and due to the intrinsic chiral symmetry in TBG, a lowest energy level related to the quantum Hall effect. The non-Abelian properties of this Hamiltonian play a central role in the electronic localization to produce the flat bands and here it is proved that the squared Hamiltonian of the chiral TBG model is equivalent to a single electron Hamiltonian inside of a non-Abelian pseudo-magnetic field produced by electrons in other layers. Therefore, the basic and fundamental elements in the physics of magic angles are determined. In particular, a study is made on these fundamental energy contributions at the Γ-point due to its relation to the recurrence of magic angles and its relationship with the Quantum Hall effect.

On Instabilities Caused by Magnetic Background Fields

We review instabilities that appear from the coupling of spin-one fields to a magnetic background in a non-Abelian theory. Such coupling results, due to asymptotic freedom in a negative quantum, contribute to the effective potential. In QCD, the Savvidy vacuum results. However, due to the tachyonic mode, such a state is not stable, and the question about the true ground state of QCD is still open. In the electroweak model, the corresponding instability is postponed to very large background fields and may be of relevance in the early universe, at best. We start with an introduction to the topic and display the necessary formulas and methods. Then, we consider the one-particle spectra of the fields in a magnetic background and the related Euler–Heisenberg Lagrangians. In addition, we discuss the potential instability connected with the anomalous moment of the electron. The main part is on the quantum correction to the energy in non-Abelian fields, including massive ones. Here, the focus is on so-called electroweak magnetism and the search for a classical solution of the field equations and their approximations by a lattice of flux tubes. Finally, we review approaches with non-homogeneous background fields and the background of an A0-field.

Decomposition of the Static Potential in SU(3) Gluodynamics

After fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics we decompose the nonabelian gauge field into the Abelian field created by Abelian monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentials in the fundamental representation and show that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. Comparison with other ways of decomposition is made.

Gauge Invariance of Non-Abelian Field Strength Correlators: The Axial Gauge Puzzle.

Many transport coefficients of the quark-gluon plasma and nuclear structure functions can be written as gauge invariant correlation functions of non-Abelian field strengths dressed with Wilson lines. We discuss the applicability of axial gauge n·A=0 to calculate them. In particular, we address issues that appear when one attempts to trivialize the Wilson lines in the correlation functions by gauge fixing. We find it is always impossible to completely remove the gauge fields n·A in Wilson lines that extend to infinity in the n direction by means of gauge transformations. We show how the obstruction appears in an explicit example of a perturbative calculation, and we also explain it more generally from the perspective of the path integral that defines the theory. Our results explain why the two correlators that define the heavy quark and quarkonium transport coefficients, which are seemingly equal in axial gauge, are actually different physical quantities of the quark-gluon plasma and have different values. Furthermore, our findings provide insights into the difference between two inequivalent gluon parton distribution functions.

FAR AND NEAR ORIGINS OF THE STANDARD MODEL IN PHYSICS OF FUNDAMENTAL INTERACTIONS (TO THE 150TH ANNIVERSARY OF F. KLEIN'S ERLANGEN PROGRAM AND TO THE 100TH ANNIVERSARY OF THE BIRTH OF C. YANG)

In connection with the 150th anniversary of F. Klein’s Erlangen program in geometry and the 100th anniversary of the birth of C. Yang, the main creator, non-Abelian gauge fields are discovered, the far and near sources of the standard in the physics of fundamental models of interactions are concluded. A distant source is the Erlangen program and its subsequent introduction of reaction to relative and classical physics. This material discusses the phenomenon of “inconceivable effectiveness of mathematics in special sciences” (J. Wigner), which becomes clearer on the basis of the “relay model” of the interaction between mathematics and physics proposed by D. Hilbert. The approximation of the Erlangen observation, which is applied to Noether's observations on the connection between meetings and meetings, is considered, as well as the application of the Erlangen observation to the history of physics. It is shown how the extension of this domain to local gauge domains is carried out by C. Yang and R. Millsakoch theories of non-Abelian field gauges (1954), which became a near source on the way to the standard and completed model in 1973-1974.

The model for non-Abelian field topology for the multilayer fractional quantum anomalous Hall device

From the recent empirical discovery of the quantum anomalous Hall effect (QAHE), the interaction of the particle with spin–orbit coupling (SOC) plays an essential role in the cause of the QAHE, which includes three terms: external, internal, and chiral symmetric terms. Then, the non-Abelian quantum field theory was adopted to analyze and prove the conjecture on the causes that can lead to the fractional quantum Hall effect (FQHE). The spontaneously topological chiral symmetry breaking is the main contribution to the FQHE, which also includes two terms: the hopping of sublattice and Coulomb energy by the interaction of many-body particles. More generally, this exciton possesses an intermediate characteristic between the Wannier regimes and displays a peculiar two-dimensional wavefunction in the three-dimensional FQHE states. Finally, a bilayer three-dimensional model is proposed to implement the FQHE on the lattice by incorporating ferromagnetic dopants into three-dimensional topological insulative thin films. This study theoretically predicts the FQHE on the basis of other reports that have experimentally verified the rationality of the proposed model in magnetic topological insulators.

Nonminimal non-Abelian quantum vector fields in curved spacetime

The quantum effective action of non-minimal vector fields with Abelian or non-Abelian gauge degrees of freedom in curved spacetime is studied. The Proca or Yang-Mills fields are coupled to a local mass-like term acting in both coordinate and gauge spaces. Pathologies due to gauge invariance in the ultraviolet are avoided through the introduction of a non-Abelian version of the Stueckelberg field. It is found that the breaking of gauge invariance induced by the mass term affects only the tree level part of the effective action. The ultraviolet divergent part of the effective action to one loop is obtained using the method of covariant symbols and dimensional regularization. Formulas are given valid for any spacetime dimension and explicit results are shown for the two-dimensional case. As already happened for a single vector field, the ultraviolet divergences are local but not of polynomial type.

Stability analysis of non-Abelian electric fields

We study the stability of fluctuations around a homogeneous non-Abelian electric field background that is of a form that is protected from Schwinger pair production. Our analysis identifies the unstable modes and we find a limiting set of parameters for which there are no instabilities. We discuss potential implications of our analysis for confining strings in non-Abelian gauge theories.

Color decorations of Jackiw-Teitelboim gravity

We introduce the colored version of Jackiw-Teitelboim (JT) gravity which is the two-dimensional dilaton gravity model with matrix-valued fields. It is straightforwardly formulated in terms of BF action with su(N, N) gauge algebra so that the standard JT gravity is embedded as su(1, 1) ⊂ su(N, N) subsector. We also elaborate on the respective metric formulation which is shown to involve the JT fields plus su(N) non-Abelian fields as well as su(N)-matrix valued metric and dilaton fields. Their interactions are governed by minimal couplings and potential terms of cubic and quartic orders involving derivatives.