4,799 research outputs found
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
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
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
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
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
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 are in
one-to-one correspondence with coherent states of a dual or magnetic group
. 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
- …