Dynamics of vacuum excitations and quark confinement in quantum field theories

A unified approach to interacting vacuum excitations and quark confinement is formulated in quantum field theories with symmetry breakdown. Vacuum excitations are shown to be coherent clouds of Goldstone bosons or gauge bosons and are interpreted as new asymptotic extended particle states. They correspond to all dynamically possible space-time dependent Bose condensations of the Goldstone bosons in a given theory. Different configurations of vacuum excitations are connected to one another by a family of invariant boson transformations. As an example, the Nambu theory of interacting vortex strings is derived from a Nambu-Heisenberg quark-gluon field theory. The quarks can be completely confined to the strings while the gluons cluster in quantized magnetic flux bundles of penetration width m_v^?1 and provide a short range interaction force.     

Coulomb gauge vacua of SU(3) gauge theory

SU(3) gauge field theory is studied in the Coulomb gauge, and the topologically distinct, but gauge equivalent, vacuum configurations are analysed. Considering the gauge transformations of the form U ε U(2) ?SU(3)/U(2), we have obtained a new class of vacuum fields characterized by the topological quantum number η = ±1.     

The Generalization of Chern-Simons Current and the Topological Tensor Current of <Emphasis Type="Italic">p</Emphasis>-Branes

To make the gauge field theory foundation of the topological current of p-branes introduced in our previous work, we present a novel topological tensor current in SO(N) gauge field theory. This non-Abelian gauge field tensor current is the straightforward generalization of the Chern-Simons topological current of strings. By making use of the SO(N) gauge potential decomposition theory and the φ-mapping topological current theory, it is proved that the p-brane is created at every isolated zero of the Clifford vector field \(\overrightarrow{\phi }(x)\) and the charges carried by p-branes are topologically quantized and labelled by the winding number of the φ-mapping.     

Superconducting strings

It is known that certain spontaneously broken gauge theories give rise to stable strings or vortex lines. In this paper it is shown that under certain conditions such strings behave like superconducting wires whose passage through astrophysical magnetic fields would generate a variety of striking and perhaps observable effects. The superconducting charge carriers may be either bosons (if a charged Higgs field has an expectation value in the core of the string) or fermions (if charged fermions are trapped in zero modes along the string, as is known to occur in certain circumstances). They might be observable as synchrotron sources or as sources of high-energy cosmic rays. If the charge carriers are ordinary quarks and leptons, the strings have important baryon number violating interactions with magnetic fields; such a string, traversing a galactic magnetic field of 10^?6 G, creates baryons (or antibaryons) at a rate of order 10¹² particles/cm of string per second.     

Chiral deformations of conformal field theories

We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the W_1+∞ algebra, that is treated in detail.     

Topology of quantum gauge fields and duality (I): Yang-Mills-Higgs system in 2 + 1 dimensions

The basic role of the representation of the gauge group in characterizing the topological excitations of the vacuum is pointed out. For SU(N) gauge fields on a lattice, the topological excitations are monopoles in the adjoint representation of the dual group ¹SU(N). This leads to a dual representation of the Yang-Mills-Higgs system in 2 + 1 dimensions. For SU(3) the deal theory in a scalar theory with discrete Weyl symmetry S₃. In the presence of adjoint Higgs fields the Weyl symmetry is broken in the Higgs phase but restored by pseudo-particles in the confinement phase.     

Monopoles and topological field theory

We present a topological quantum field theory for magnetic monopoles in an SU(N) Yang-Mills-Higgs model. This field theory is obtained by gauge fixing the topological action defining the monopole charge. This work extends to the three-dimensional case the quantization of invariant polynomials in four dimensions. We choose the Bogomolny self-duality equations as gauge conditions for the magnetic monopole topological field theory. In this way the geometrical equation discussed e.g. in Atiyah and Hitchin's work are recovered as ghost equations of motion. We give the cocycles of the corresponding topological symmetry. In the N→∞ limit interesting phenomena occur. The functional integration is forced to cover only the moduli space and the role of the ghosts stemming from the gauge fixing process is to provide a smooth semiclassical approximation.     

Topology of the gauge condition and new confinement phases in non-abelian gauge theories

The gauge-fixing constraint in a gauge field theory is crucial for understanding both short-distance and long-distance behavior of non-abelian gauge field theories. We define what we call “non-propagating” gauge conditions such as the unitary gauge and “approximately non-propagating” or renormalizable gauge conditions, and study their topological properties. By first fixing the non-abelian part of the gauge ambiguity we find that SU(N) gauge theories can be written in the form of abelian gauge theories with N ? 1 fold multiplicity enriched with magnetic monopoles with certain magnetic charge combinations. Their electric chargesare governed by the instanton angle θ.If θ is continuously varied from 0 to 2π and a confinement mode is assumed for some θ, then at least one phase-transition must occur. We speculate on the possibility of new phases: e.g., “oblique confinement,” where $\text{θ ? π}$, and explain some peculiar features of this mode. In principle there may be infinitely many such modes, all separated by phase transition boundaries.     

On a soluble model of an antiferromagnetic chain with alternating interactions and magnetic moments

The one-dimensional anisotropic XY model with alternating nearest-neighbour interactions and magnetic moments is investigated. The singularities of the susceptibility χ_zz in the ground state are studied in detail. In the general anisotropic case χ_zz can exhibit two logarithmic singularities at two different values of the applied magnetic field b. If the interactions satisfy a certain relation which will be reffered to as the pseudoisotropic condition (which includes the isotropic case), χ_zz can have two power-$\text{1}\text{2}$ singularities at the upper side of the lower critical field and the lower side of the upper critical field. Deviations from this behaviour which occur for special values of the interaction constants are discussed in some detail. Finally the specific heat is studied in the low- and high-temperature limits.     

Topological quantization of mass in extended gauge theories with a monopole

Alvarez's treatment of topological charge quantization is generalized to include extended objects like the Dirac string in the presence of a magnetic pole. We rederive the topological mass quantization of the Abelian gauge field in (2+1)-dimensional spacetime previously derived by Henneaux and Teitelboim. A plausible argument is given for the general 2p + 1 cases in which the present method works.     

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U (n). As the result, one can create a theory of particle evolution that is gauge-invariant with regards to the group Uⁿ (1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U (1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping, and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory, the article considers a number of important particular examples, both known and new.     

球对称的SU2规范场和磁单极的规范场描述

本文讨论球对称的SU₂规范场,证明了满足最一般的球对称定义的SU₂规范场只能有三种基本类型:(1)同步球对称规范场;(2)狭义球对称规范场;(3)化约为U₁子群的球对称规范场。文中详细讨论了球对称的带同位旋向量场(Higgs场)的SU₂规范场,完全决定了它们的类型。如果把这种场看成为由电磁场和带电矢介子构成,那末就有如下的结论:如果磁单极所含的磁荷是最小单位的m倍,当|m|>1时,球对称的带Higgs场的SU₂规范场只能是纯电磁场,而不能有带电矢介子场出现。但当m=0,±1时,球对称的带电矢介子场是可以出现的。从而可见,具有非单位磁荷的磁单极隐含了某种破坏球对称的因素。     

M theory and singularities of exceptional holonomy manifolds

M theory compactifications on G₂ holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory.     

Monopole and topological electron dynamics in adiabatic spintronic and graphene systems

A unified theoretical treatment is presented to describe the physics of electron dynamics in semiconductor and graphene systems. Electron spin's fast alignment with the Zeeman magnetic field (physical or effective) is treated as a form of adiabatic spin evolution which necessarily generates a monopole in magnetic space. One could transform this monopole into the physical and intuitive topological magnetic fields in the useful momentum (K) or real spaces (R). The physics of electron dynamics related to spin Hall, torque, oscillations and other technologically useful spinor effects can be inferred from the topological magnetic fields in spintronic, graphene and other SU(2) systems.     

A visualization of the SU(2) vacuum on the lattice

Configurations of pure SU(2) gauge field theory on lattice are transformed to Landau gauge. After Fourier transformation, large momentum amplitudes are suppressed (filtered) by a variable amount, and the configurations are transformed back to x-space. Spectacular peaks in electric and magnetic field strengths are found, which share many properties with either almost pointlike instantons or with extended anti-instantons. The environment around those peaks are visualized with respect to the action, to the topological charge density, to the gauge fields and to electric and magnetic field strengths. The density of the peaks is of order 1 fm^–4, and it scales according to the string tension under a variation of the coupling constant. The evolution of the peaks under the amount of Fourier filtering is visualy compared to the evolution under cooling, and the gauge dependence of the peaks is discussed. Advantages and shortcomings of this method are discussed, with emphasis on possible strong distortions of the action and topological charge density, which become gauge dependent. Finally, I compare the character of the SU(2)-configurations to those of noncompact abelian theory.     

The coupling of Chern–Simons theory to topological gravity

We couple Chern–Simons gauge theory to 3-dimensional topological gravity with the aim of investigating its quantum topological invariance. We derive the relevant BRST rules and Batalin–Vilkovisky action. Standard BRST transformations of the gauge field are modified by terms involving both its anti-field and the super-ghost of topological gravity. Beyond the obvious couplings to the metric and the gravitino, the BV action includes hitherto neglected couplings to the super-ghost. We use this result to determine the topological anomalies of certain higher ghost deformations of SU(N)$\mathit{SU}(N)$ Chern–Simons theory, introduced years ago by Witten. In the context of topological strings these anomalies, which generalize the familiar framing anomaly, are expected to be cancelled by couplings of the closed string sector. We show that such couplings are obtained by dressing the closed string field with topological gravity observables.     

Analytic study of θ vacua on the lattice

A new definition of the topological charge density for four-dimensional lattice gauge theory is given. Using a systematic expansion we find a cusp in the vacuum energy at θ = π signaling the spontaneous breaking of CP there. Unlike its two-dimensional analogue (QED₂), QCD confines at θ = π. As a by-product an expression for the topological mass term for (2+1)-dimensional lattice gauge theory is obtained.