Liquid-crystal defects and confinement in Yang-Mills theory

It has been shown that, in the Landau gauge of the SU(2) Yang-Mills theory, the residual global symmetry supports the existence of topological vortices which resemble disclination defects in nematic liquid crystals and Alice (half-quantum) vortices in superfluid ³He in the A-phase. The theory also possesses half-integer and integer-charged monopoles, which are analogous to the point-like defects in nematic crystal and in liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles. The text was submitted by the author in English.     

Fermions and spherically symmetric monopoles

The interaction of fermions with monopoles is analyzed for general spherically symmetric monopoles of arbitrary strength and massless fermions in arbitrary representations of the gauge group. The results are based on a solution to the Dirac equation in the field of the monopole, valid in the point limit and in all partial waves. The partial waves in which non-conservation of global charges may occur are identified. A two-dimensional lagrangian is derived, which includes the Coulomb interactions generated by the complete abelian subgroup of the unbroken gauge group. The fermions are represented by a set of doublets with a boundary condition that reflects the structure of the core. We derive a simple formula for the conservation laws of this model which determine all scattering processes completely. The results have a consistent interpretation in terms of anomalies and field configurations with non-trivial winding number. We give an explicit construction of the zero modes for all helicity-violating multi-fermion condensates. The formalism is applied to several higher strength monopoles in SO(10) based models.     

Torsional Weyl-Dirac Electrodynamics

Issuing from a geometry with nonmetricity and torsion we build up a generalized classical electrodynamics. This geometrically founded theory is coordinate covariant, as well as gauge covariant in the Weyl sense. Photons having arbitrary mass, intrinsic magnetic currents, (magnetic monopoles), and electric currents exist in this framework. The field equations, and the equations of motion of charged (either electrically or magnetically) particles are derived from an action principle. It is shown that the interaction between magnetic monopoles is transmitted by massive photons. On the other hand, the photon is massive only in the presence of magnetic currents. We obtained a static spherically symmetric solution, describing either the Reissner-Nordstrom metric of an electric monopole, or the metric and field of a magnetic monopole. The latter must be massive. In the absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory.     

Massless monopoles and multi-pronged strings

We investigate the role of massless magnetic monopoles in the N=4 supersymmetric Yang-Mills Higgs theories. They can appear naturally in the 1/4-BPS dyonic configurations associated with multi-pronged string configurations. Massless magnetic monopoles can carry nonabelian electric charge when their associated gauge symmetry is unbroken. Surprisingly, massless monopoles can also appear even when the gauge symmetry is broken to abelian subgroups.     

Exact magnetic monopole solutions in Yang-Mills and unified gauge theories

We study the magnetic monopoles in non-Abelian gauge theories. The exact static, spherically symmetric solutions of the magnetic monopoles in both Yang-Mills and unified gauge theories are obtained. The energyE of the static system is calculable and it is either zero or infinite. The existence of the magnetic monopole solution is a consequence of symmetry rather than dynamics. We propose a new definition of the electromagnetic field tensor, which relates the static solution of gauge fields and the magnetic monopole solution. Experimental implications are discussed.     

Evidence for monopoles in the quantizedSU(2) lattice vacuum: A study at finite temperature

InSU(2) gauge theory colour confinement occurs if the vacuum condenses into a coherent monopole plasma. To verify this picture, the first question to be answered is whether the vacuum supports monopoles at all. Since we expect the monopoles to be dilute and massive in the deconfinement, phase, we begin the search there. The method relies on cooling equilibrium lattice gauge field configurations—which are generated at the appropriate temperature—until the underlying semiclassical solutions emerge. We then pass to the confinement region and ask whether the monopoles condense. Finally, we repeat the procedure for gauge groupSU(3). The results confirm our expectations.     

Configurations of SO(3) monopoles with multiple magnetic charge

In this paper we consider configurations of monopoles with multiple magnetic charge in nonabelian gauge theory. Explicit gauge transformations are constructed which eliminate the string singularities for single monopoles of multiple magnetic charge, and for an arbitrary number of monopoles lying along a line. The question of finding nonsingular solutions is discussed.     

Monopole charges in unified gauge theories

Monopole charges, being global quantities, depend on the gauge group of a theory, which in turn is determined by the representations of all its fields. For example, chromodynamics in its present form when combined with electrodynamics has as its gauge group not SU(3) × U(1) but a “smaller” group U(3). The specification of monopole charges for a theory can thus be quite intricate. We report here the result of an investigation in several current gauge theories. Of particular interest is the possible existence in some theories of monopoles carrying multiplicative charges. As a by-product, we clarify some earlier assertions in the literature which seem to us incorrect.     

Magnetic monopoles, alive

We review recent developments in understanding the physics of the magnetic monopoles in unbroken non-Abelian gauge theories. Since numerical data on the monopoles are accumulated in lattice simulations, the continuum theory is understood as the limiting case of the lattice formulation. We emphasize physical effects related to the monopoles. In particular, we discuss the monopole-antimonopole potential at short and larger distances as well as a dual formulation of the gluodynamics, relevant to the physics of the confinement.     

Triplication of SU(5) Monopoles

We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5)-->[SU(3) x SU(2) x U(1)]/Z(3) x Z(2) symmetry breaking. We find that there are three solutions that are gauge equivalent but, as we argue, would correspond to physically distinct degrees of freedom in the dualized version of the model. The triplication of monopoles could help us understand the observed family structure of standard model particles.     

Monopoles, instantons and chiral condensate in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD at finite temperature on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons. Studies are performed in both pure and full QCD and in both the confinement and deconfinement phase. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover the correlation of monopole loops and instantons with the chiral condensate is investigated. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.     

Internal structure of the monopoles

The non-abelian monopoles are shown to form linear multiplets under the color reflection symmetry of the original gauge group. This implies that as far as the gauge symmetry is kept unbroken only the singlet combinations of the monopoles may be admitted in the physical sector.     

Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory

We study Bogomolny equations on ℝ²×?¹. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk?hler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius. Received: 20 July 2000 / Accepted: 29 November 2000     

电磁学与电动力学中的磁单极-Ⅱ

本系列文章一共4篇,在电磁学和电动力学框架内用尽量科普的方式分别介绍磁单极的若干奇特性质.本篇文章主要介绍狄拉克磁单极是如何展示矢量势的规范变换的.我们首先简要介绍规范变换与规范对称性及狄拉克磁单极与狄拉克弦,然后讨论狄拉克磁单极与规范变换的联系.我们显式演示狄拉克弦摆动产生的规范变换,弦摆动区域对场点所张的立体角正比于规范变换的变换函数.磁偶极子则可以由两个无穷靠近的正反狄拉克磁单极构成.相应两条狄拉克弦位置的变化都对应磁偶极子矢量势的规范变换,特别当两条弦重合时弦效应相互抵消,只剩下纯的磁偶极子.传统的由磁偶极子产生的矢量势的规范变换则可以图像化为组成磁偶极子的正反狄拉克磁单极的狄拉克弦的摆动.我们显式地计算了位于坐标原点弦为直线的狄拉克磁单极,并进一步构造了没有奇异的吴大峻-杨振宁磁单极.     

Kertész line and embedded monopoles in QCD

We propose a new class of defects in QCD which can be viewed as embedded monopoles made of quark and gluon fields. These objects are explicitly gauge invariant and they closely resemble the Nambu monopoles in the standard electroweak model. We argue that the "embedded QCD monopoles" are proliferating in the quark-gluon plasma phase while in the low-temperature hadronic phase the spatial proliferation of these objects is suppressed. At realistic quark masses and zero chemical potential the hadronic and quark-gluon phases are generally believed to be connected by a smooth crossover across which all thermodynamic quantities are nonsingular. We argue that these QCD phases are separated by a well-defined boundary-known as the Kertész line in condensed matter systems-associated with the onset of the proliferation of the embedded QCD monopoles in the quark-gluon plasma phase.     

Colored magnetic monopoles

We extend Dirac's theory of magnetic monopoles to the case of non-Abelian color gauge groups. Exact classical solution is obtained by making use of the gauge-independent method of Yang-Mills field. The case of broken gauge symmetry is also briefly discussed.     

Magnetic monopoles in gauge theories

Magnetic monopoles in gauge theories are investigated. Let G be the gauge group and H the group of symmetries which are not spontaneously broken. The existence of magnetic monopoles is proved in the case when the group G has a compact covering group but the covering group of H is non-compact.     

Geometrical aspects of magnetic monopoles

The possible topological structures of elementary particles have been investigated to explore the possibility of the existence of magnetic monopoles. It is pointed out that when an elementary charged particle is depicted as an extended body such that the orientation of the internal space (internal helicity) defines the fermion number, the global conservation of this does not allow the existence of a magnetic monopole. Again it is argued that when anisotropy is introduced in the microlocal space-time depicting the internal space of hadrons, this gives rise to the internal symmetry algebra and no non-Abelian gauge fields and Higgs scalars are necessary to have a grand unified scheme of interactions. This avoids theSU ₂ and GUT monopoles. Besides, in this formalism, baryon number corresponds to the orientation or internal helicity of the composite system and the global conservation of this quantum number is found to be a consequence of Lorentz invariance. This forbids the existence of any sort of cosmological monopole in this Lorentz invariant Universe.     

Universal properties of U(1) gauge theories

The previously known analogies between four-dimensional compact U(1) lattice gauge theories and the two-dimensional planar model are extended to a number of other results. We show that the monopoles in the gauge theory renormalize the coupling constant α by an amount proportional to the susceptibility of the monopole gas. Confinement occurs when this susceptibility diverges. We argue that α is analogous to the critical exponent η of the planar model, and that the transition occurs at a universal critical value α_c.We also define an analogue of the superfluid density for the gauge theory, in terms of the dependence of the free energy on the boundary conditions, and show that it is universally related to α. Finally, we show that the same physics emerges from a continuum U(1) theory with real magnetic monopoles.