Constructing non-Abelian vortices with arbitrary gauge groups

We construct the general vortex solution in the color–flavor-locked vacuum of a non-Abelian gauge theory, where the gauge group is taken to be the product of an arbitrary simple group and U(1)$U(1)$. Use of the holomorphic invariants allows us to extend the moduli-matrix method and to determine the vortex moduli space in all cases. Our approach provides a new framework for studying solitons of non-Abelian varieties with various possible applications in physics.     

Bound States of Monopoles and Dyons with Spin-1/2 Particles in SU(2) Gauge Theory Under Moduli Space Approximation

Energy spectrum and degeneracy associated with bound states of monopoles and dyons in non-Abelian gauge theory has been investigated and it is shown that energy levels expand due to the presence of additional degeneracies. Splitting of energy level of dyonium in presence of external magnetic and electric field has also been analyzed confirming the presence of additional degeneracy levels of the system. In addition, the study of behaviour of a fermion moving in the field of non-Abelian dyon in moduli space under SU(2) gauge potential has been undertaken and energy eigen values for the system are carried out. Detailed analysis of relativistic correction in fermion-dyon system in moduli space is presented and angular momentum operators of the system are derived, which demonstrates that besides the contribution of Higgs field, the interaction of spin and orbital angular momentum of moving fermion also contributes to the energy operator.     

规范场和爱因斯坦

文章讨论的主题是现代非亚贝尔规范场的理论思想．文章说明了这个理论思想是承传、推广和拓展了爱因斯坦的物理思想、目标和原则．规范场理论把爱因斯坦后半生努力奋斗而未能达到的目标提到现实，更加迫近和部分地圆了爱因斯坦的梦想。     

Radiative Corrections to Non-Abelian Gauge Theory in Homogeneous Self-Dual Backgrounds

We study the Euclidean version of non-Abelian gauge theories in homogeneous background fields with due regard of negative and zero modes of the gauge field kernel. For general gauge group and general background but without external currents we prove a relation between the propagators belonging to different gauge fixings. Specializing to a self-dual homogeneous background we derive nonperturbatively the propagators. Next we calculate the matter field contribution to the renormalized polarization tensor using a modified dimensional regularization scheme. We prove the validity of a modified Ward identity.     

Diquark condensation in dense adjoint matter

We study SU(2) lattice gauge theory at non-zero chemical potential with one staggered quark flavor in the adjoint representation. In this model the fermion determinant, although real, can be both positive and negative. We have performed numerical simulations using both hybrid Monte Carlo and two-step multibosonic algorithms, the latter being capable of exploring sectors with either determinant sign. We find that the positive determinant sector behaves like a two-flavor theory, with the chiral condensate rotating into a two-flavor diquark condensate for , implying a superfluid ground state. Good agreement is found with analytical predictions made using chiral perturbation theory. In the ‘full’ model there is no sign of either onset of baryon density or diquark condensation for the range of chemical potentials we have considered. The impact of the sign problem has prevented us from exploring the true onset transition and the mode of diquark condensation, if any, for this model. Received: 28 September 2001 / Published online: 23 November 2001     

Quantum fluctuations and dynamical chaos: An effective potential approach

We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.     

Non-Abelian Gauge Theory in the Lorentz Violating Background

In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.     

Non-Abelian gauge potentials driven localization transition in quasiperiodic optical lattices

Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential.     

Long-Range Behavior of Dual-Restricted QCD Vacuum

We analyze the geometrical structure of the local non-Abelian gauge theory in terms of the magnetic symmetry, using the resemblance between the non-Abelian gauge formulations and Einstein's theory of gravitation in a higher dimensional unified space. The mathematical foundation of dual QCD in fiber bundle form is then discussed and used for the analysis of the important problem of color confinement in QCD. The associated Lagrangian formulation in magnetic gauge is shown to lead to dual dynamics due to the emergence of the topological charges of magnetic nature. The dynamical breaking of magnetic symmetry is shown to lead to the magnetic condensation of the QCD vacuum. A state of the dual superconductivity in the QCD vacuum is then shown to evolve which ultimately pushes the QCD vacuum to the confining phase. The flux tube structure of the magnetically condensed QCD vacuum is analyzed by computing the asymptotic string solutions of the field equations. The energy content of such confining structures is computed and analyzed in terms of its logarithmic and linear nature.     

Universal reconnection of non-Abelian cosmic strings

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.     

A covariant approach to gauged 2D self-dual fields

We obtain a non-Abelian version of a theory involving vector and tensor gauge fields interacting via a massive topological coupling, besides the nonminimun one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to make compatible gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case.     

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which the obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. We formulate both a special relativistic and a general relativistic versions of Feynman's derivation. Especially in the general relativistic version we prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. We also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context.     

Pion condensation in a medium with massive quarks in an external spherically symmetrical non-Abelian chromomagnetic field

We consider pion condensation in a flavor asymmetric quark medium with massive quarks in the external spherically symmetric non-Abelian chromomagnetic field. It is shown that the external field is a catalyzing factor for the occurrence of pion condensation, while the finite quark masses prevent the emergence of this phenomenon.     

Global charges of stationary non-Abelian black holes

We consider stationary axially symmetric black holes in SU(2) Einstein-Yang-Mills-dilaton theory. We present a mass formula for these stationary non-Abelian black holes, which also holds for Abelian black holes. The presence of the dilaton field allows for rotating black holes, which possess nontrivial electric and magnetic gauge fields, but do not carry a non-Abelian charge. We further present a new uniqueness conjecture.     

Late time phase transition as dark energy

We show that the dark energy field can naturally be described by the scalar condensates of a non-abelian gauge group. This gauge group is unified with the standard model gauge groups and it has a late time phase transition. The small phase transition explains why the positive acceleration of the universe is occurring only recently. The model hasno free parameters but for the matter content of the group. The initial energy density at the unification scale and at the condensation scale are fixed by the number of degrees of freedom of the gauge group.     

Non-Abelian vortex in four dimensions as a critical superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional supersymmetric QCD with the gauge group, N _f = 4 quark flavors and the Fayet–Iliopoulos term. Under certain conditions, the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli, the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a twodimensional sigma model with the target space ?⁴ × Y ₆, where Y ₆ is a non-compact Calabi–Yau conifold. The closed string states that emerge in four dimensions (4D) are identified with hadrons of 4D bulk N= 2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole–monopole baryon of the 4D theory (at strong coupling).     

Construction of non-Abelian walls and their complete moduli space

We present a systematic method to construct exactly all Bogomol'nyi-Prasad-Sommerfield multiwall solutions in supersymmetric U(N(C)) gauge theories in five dimensions with N(F) hypermultiplets in the fundamental representation for infinite gauge coupling. The moduli space of these non-Abelian walls is found to be the complex Grassmann manifold SU(N(F)) divided by SU(N(C))xSU(N(F)-N(C))xU(1) endowed with a deformed metric.