Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups

Magnetic monopole solutions for an arbitrary compact simple gauge group are considered in the Prasad-Sommerfield limit. For each group and choice of symmetry breaking there is a set of fundamental monopoles with minimal topological charges and possessing no internal degrees of freedom; the number of these is less than or equal to the rank of the gauge group. It is shown that if the unbroken gauge group is abelian, all solutions with higher topological charges belong to p-parameter families, where p is the number of position and group orientation parameters needed to describe a set of non-interacting fundamental monopoles with the given topological charge. It is argued that these solutions, some examples of which are given, should therefore be interpreted as multimonopole configurations. An extension of these results to the case of a non-albelian unbroken gauge symmetry is conjecture and shown to be valid for a number of examples.     

Topological Geon Black Holes in Einstein-Yang-Mills Theory

We construct topological geon quotients of two families of Einstein-Yang-Mills black holes. For Künzle??s static, spherically symmetric SU(n) black holes with n?>?2, a geon quotient exists but generically requires promoting charge conjugation into a gauge symmetry. For Kleihaus and Kunz??s static, axially symmetric SU(2) black holes a geon quotient exists without gauging charge conjugation, and the parity of the gauge field winding number determines whether the geon gauge bundle is trivial. The geon??s gauge bundle structure is expected to have an imprint in the Hawking-Unruh effect for quantum fields that couple to the background gauge field.     

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.     

不可易规范场的对偶荷

本文讨论了不可易SU(2)规范场的各种规范不变物理量——电荷、对偶荷(磁荷)、电磁场以及有质量矢粒子场的表达式与关系,特别是对偶荷(磁荷)与电荷算符同位旋方向的大范围拓扑性质的关系。     

Investigating the topological structure of quenched lattice QCD with overlap fermions using a multi-probing approximation

The topological charge density and topological susceptibility are determined by a multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and compare it with results from the all-scale topological density. The results are consistent.Random permuted topological charge density is used to check whether these structures represent underlying ordered properties. The pseudoscalar glueball mass is extracted from the two-point correlation function of the topological charge density. We study 3 ensembles of different lattice spacing a with the same lattice volume 16~3×32. The results are compatible with the results of all-scale topological charge density, and the topological structures revealed by multi-probing are much closer to all-scale topological charge density than those from eigenmode expansion.     

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.     

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.     

Topology and lattice gauge fields

A general discussion of the topology of continuum gauge fields and the problems involved in defining and computing the topology of a lattice gauge field configuration is given. Two definitions of the topological charge for 4-dimensional SU(n) lattice gauge theory are presented. The first of these is geometrically the most straightforward, the second the most useful for efficient numerical calculations.     

The soliton supermultiplet in 4 + 1 dimensions

We consider the SO(4) = SU(2) ? USp(2) Clifford algebra, obtained by the supersymmetry algebra for the N = 2 supersymmetric Yang-Mills theory in 4+1 dimensions, which, in the phase of unbroken gauge symmetry, has a topological charge as central charge. We find that, even if the Higgs mechanism is absent, the massive soliton supermultiplet contains the same number of states as the massless supermultiplet of elementary particles.     

Gauge fixing, families index theory, and topological features of the space of lattice gauge fields

The families index theory for the overlap lattice Dirac operator is applied to derive topological features of the space of SU(N) lattice gauge fields on the 4-torus: the topological sectors, specified by the fermionic topological charge, are shown to contain noncontractible even-dimensional spheres when N3, and noncontractible circles in the N=2 case. We describe how certain obstructions to the existence of gauge fixings without the Gribov problem in the continuum setting correspond on the lattice to obstructions to the contractibility of these spheres and circles. We also point out a canonical connection on the space of lattice gauge fields with monopole-like singularities associated with the spheres.     

On the topological charge concentrated at a point

For SU(2) gauge fields over the 4-dimensional sphere with a finite number of points x₁, x₂, ..., and x_N removed, there are gauge transformations which modify the topological charge concentrated at x_j by adding n_j, where n₁, n₂, …, and n_N. are integers such that Σ^N_{j = 1}n_j = 0. However, the reduction modulo Z of the topological charge at a point is well defined, being given in terms of the secondary characteristic classes of Chern and Simons, except when the topological charge is indeterminate.     

String-like topological excitations of the electromagnetic field

In order to analyze the topological properties of an arbitrary configuration of the electromagnetic field, its strength F_μν is expressed in terms of new auxiliary fields which replace the gauge potential A_μ. These new fields have only physical singularities even in the presence of monopoles (no Dirac strings) and exhibit a new local O(1, 1) symmetry which replaces the gauge invariance. Boundary conditions on these fields may induce localized string-like singularities or topological defects which act as sources of magnetic field. A typical defect which emerges is a sort of tadpole formed by a non-quantized monopole attached to one or more magnetic strings of finite length. For topological reasons the total magnetic charge is quantized.     

The topological meaning of non-abelian anomalies

We show how the non-abelian anomaly for gauge fields coupled to Weyl fermions in 2n dimensions is related to the non-trivial topology of gauge orbit space. The form of the anomaly and its normalization are shown to follow from a familiar index theorem for a certain (2n + 2)-dimensional Dirac operator. We are thus able to recover and give topological meaning to a variety of results concerning anomalies in 4- and higher-dimensional theories.     

Lattice θ vacua

We study some aspects of θ vacua by Monte-Carlo simulations of the SU(2) lattice gauge theory using a definition proposed recently for the total lattice topological charge. We find no phase transition up to θ = 0.8π. Beyond this point, limited statistical accuracy prevents a definite conclusion. Our results are in surprisingly good agreement with the dilute gas picture.     

Various topological excitations in the SO (4) gauge field in higher dimensions

Following the original analysis of Zhang and Hu for the 4-dimensional generalization of Quantum Hall effect, there has been much work from different viewpoints on the higher dimensional condensed matter systems. In this paper, we discuss three kinds of topological excitations in the SO (4) gauge field of condensed matter systems in 4-dimension—the instantons and anti-instantons, the ’t Hooft-Polyakov monopoles, and the 2-membranes. Using the ?-mapping topological theory, it is revealed that there are 4-, 3-, and 2-dimensional topological currents inhering in the SO (4) gauge field, and the above three kinds of excitations can be directly and explicitly derived from these three kinds of currents, respectively. Moreover, it is shown that the topological charges of these excitations are characterized by the Hopf indices and Brouwer degrees of ?-mapping.     

On the light-cone formulation of classical non-abelian gauge theory

For a classical Yang-Mills field which is periodic in the longitudinal light-cone coordinate: (a) a gauge condition is formulated, (b) the presence of field singularities in this gauge is shown, and (c) the relevance of these singularities to the topological charge is demonstrated.Also of the Science Sector, UNESCO     

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.     

Topological susceptibility from overlap fermion

We numerically calculate the topological charge of the gauge configurations on a finite lattice by the fermionic method with overlap fermions. By using the lattice index theorem, we identify the index of the massless overlap fermion operator to the topological charge of the background gauge configuration. The resulting topological susceptibility χ is in good agreement with the anticipation made by Witten and Veneziano.     

Lorentz anomaly in arbitrary dimensions

It is shown that the Lorentz invariance is broken in gauge theories of chiral Weyl fermions in flat space-time via one-loop quantum corrections. Abelian gauge fields contribute to this anomaly in even dimensions larger than or equal to four and non-Abelian gauge fields do in even dimensions larger than or equal to six. The anomaly is proportional toD/2–1 power to the charge, whereD is a number of space-time dimensions.