To be or not to be? Magnetic monopoles in non-abelian gauge theories

Magnetic monopoles form an inspiring chapter of theoretical physics, covering a variety of surprising subjects. We review their role in non-abelian gauge theories. An expose of quite exquisite physics derived from a hypothetical particle species, because the fact remains that in spite of ever more tempting arguments from theory, monopoles have never reared their head in experiment. For many relevant particulars, references to the original literature are provided.Comment: 34 pages, 7 figures, Contribution to "Fifty Years of Yang- Mills Theory", edited by G. 't Hooft. Some extra references have been added in the revised versio

Development of multiple media documents

Development of documents in multiple media involves activities in three different fields, the technical, the discoursive and the procedural. The major development problems of artifact complexity, cognitive processes, design basis and working context are located where these fields overlap. Pending the emergence of a unified approach to design, any method must allow for development at the three levels of discourse structure, media disposition and composition, and presentation. Related work concerned with generalised discourse structures, structured documents, production methods for existing multiple media artifacts, and hypertext design offer some partial forms of assistance at different levels. Desirable characteristics of a multimedia design method will include three phases of production, a variety of possible actions with media elements, an underlying discoursive structure, and explicit comparates for review

Simulations of Alice Electrodynamics on a Lattice

In this paper we present results of numerical simulations and some (analytical) approximations of a compact U(1)\ltimes\ZZ_2 lattice gauge theory, including an extra bare mass term for Alice fluxes. The subtle interplay between Alice fluxes and (Cheshire) magnetic charges is analysed. We determine the phase diagram and some characteristics of the model in three and four dimensions. The results of the numerical simulations in various regimes, compare well with some analytic approximations.Comment: 17 pages, 16 figures; minor change

Condensate-induced transitions between topologically ordered phases

We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetrybreaking phase transitions which applies to phases with topological excitations described by quantum groups or modular tensor categories. This enables us to deal with phases whose quasiparticles have noninteger quantum dimensions and obey braid statistics. Many examples of such phases can be constructed from two-dimensional rational conformal field theories, and we find that there is a beautiful connection between quantum group symmetry breaking and certain well-known constructions in conformal field theory, notably the coset construction, the construction of orbifold models, and more general conformal extensions. Besides the general framework, many representative examples are worked out in detail

The breaking of quantum double symmetries by defect condensation

In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one existing in the literature, and therefore extends the number of possible breaking patterns that can be described consistently. We start by recalling why the extended symmetry notion of quantum double algebras is an optimal tool when analyzing a wide variety of two dimensional physical systems including quantum fluids, crystals and liquid crystals. The power of this approach stems from the fact that one may characterize both ordinary and topological modes as representations of a single (generally non-Abelian) Hopf symmetry. In principle a full classification of defect mediated as well as ordinary symmetry breaking patterns and subsequent confinement phenomena can be given. The formalism applies equally well to systems exhibiting global, local, internal and/or external (i.e. spatial) symmetries. The subtle differences in interpretation for the various situations are pointed out. We show that the Hopf symmetry breaking formalism reproduces the known results for ordinary (electric) condensates, and we derive formulae for defect (magnetic) condensates which also involve the phenomenon of symmetry restoration. These results are applied in two papers which will be published in parallel.Comment: 65 pages, 7 figures, correction in table 3, updated reference

Quantumgroups in the Higgs Phase

In the Higgs phase we may be left with a residual finite symmetry group H of the condensate. The topological interactions between the magnetic- and electric excitations in these so-called discrete H gauge theories are completely described by the Hopf algebra or quantumgroup D(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebra D(H) into a quasi-Hopf algebra by means of a 3-cocycle H. Consequently, the finite number of physically inequivalent discrete H gauge theories obtained in this way are labelled by the elements of the cohomology group H^3(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions. (Invited talk given by Mark de Wild Propitius at `The III International Conference on Mathematical Physics, String Theory and Quantum Gravity', Alushta, Ukraine, June 13-24, 1993. To be published in Theor. Math. Phys.)Comment: 19 pages in Latex, ITFA-93-3

Nematic phases and the breaking of double symmetries

In this paper we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e. as representations of a single (non-Abelian) Hopf symmetry. The method that exists in the literature (and is developed in a paper published in parallel) allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra and the symmetry algebra characterizing the effective ``low energy'' theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two dimensional quantum fluids, crystals and liquid crystals.Comment: 17 pages, 2 figures, correction to table VII, updated reference

Theory of Topological Edges and Domain Walls

We investigate domain walls between topologically ordered phases in two spatial dimensions. We present a method which allows for the determination of the superselection sectors of excitations of such walls and which leads to a unified description of the kinematics of a wall and the two phases to either side of it. This incorporates a description of scattering processes at domain walls which can be applied to questions of transport through walls. In addition to the general formalism, we give representative examples including domain walls between the Abelian and non-Abelian topological phases of Kitaev’s honeycomb lattice model in a magnetic field, as well as recently proposed domain walls between spin polarized and unpolarized non-Abelian fractional quantum Hall states at different filling fractions