On a core instability of 't Hooft Polyakov monopoles

We discuss a core instability of 't Hooft Polyakov monopoles in Alice electrodynamics type of models in which charge conjugation symmetry is gauged. The monopole may deform into a toroidal defect which carries an Alice flux and a (non-localizable) magnetic Cheshire charge.Comment: 7 pages, 4 figure

Topological entanglement entropy relations for multi phase systems with interfaces

We study the change in topological entanglement entropy that occurs when a two-dimensional system in a topologically ordered phase undergoes a transition to another such phase due to the formation of a Bose condensate. We also consider the topological entanglement entropy of systems with domains in different topological phases, and of phase boundaries between these domains. We calculate the topological entropy of these interfaces and derive two fundamental relations between the interface topological entropy and the bulk topological entropies on both sides of the interface.Comment: 4 pages, 3 figures, 2 tables, revte

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 symmetry breaking 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 non-integer 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.Comment: 27 pages, 3 figures, RevTe

S-duality in SU(3) Yang-Mills Theory with Non-abelian Unbroken Gauge Group

It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group $H$ are in one-to-one correspondence with coherent states of a dual or magnetic group $\tilde H$. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2,Z)-mapping between sectors which leaves the fusion rules invariant.Comment: 27 pages, harvmac, amssym, one eps figure; minor misprints corrected and title amende

The modular S-matrix as order parameter for topological phase transitions

We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular $S$-matrix, also in the broken phase. From the measured broken $S$-matrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular $S$-matrix can be employed as a matrix valued non-local order parameter from which the low-energy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions we studied a non-abelian anyon model based on the quaternion group $H=\bar{D_2}$ of order eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established.Comment: 37 page

Noncompact dynamical symmetry of a spin-orbit coupled oscillator

We explain the finite as well as infinite degeneracy in the spectrum of a particular system of spin-1/2 fermions with spin-orbit coupling in three spatial dimensions. Starting from a generalized Runge-Lenz vector, we explicitly construct a complete set of symmetry operators, which span a noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only involves a particular, infinite, so called singleton representation. In the branch where orbital and spin angular momentum are aligned the full representation appears, constituting a 3D analogue of Landau levels. Anti-aligning the spin leads to a finite degeneracy due to a truncation of the singleton representation. We conclude the paper by constructing the spectrum generating algebra of the problem

Diagrammatics for Bose condensation in anyon theories

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs). These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase, such that they can be evaluated using the data of the original theory and a limited number of VLCs. Some representative examples are worked out in detail.Comment: 20 pages, 1 figure, many diagram

Tensor product representations of the quantum double of a compact group

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the action of the R-matrix, and their decomposition into irreducible *-representations. The example of D(SU(2)) is treated in detail, with explicit formulas for direct integral decomposition (`Clebsch-Gordan series') and Clebsch-Gordan coefficients. We point out possible physical applications.Comment: LaTeX2e, 27 pages, corrected references, accepted by Comm.Math.Phy

Defect mediated melting and the breaking of quantum double symmetries

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference