50 research outputs found
Confinement in partially broken abelian Chern-Simons theories
Planar Chern-Simons (CS) theories in which a compact abelian gauge group U(1)
x U(1) is spontaneously broken to U(1) x Z_N are investigated. Among other
things, it is noted that the theories just featuring the mixed CS term coupling
the broken to the unbroken U(1) gauge fields in general exhibits an interesting
form of confinement: only particles carrying certain multiples of the
fundamental vortex flux unit and certain multiples of the fundamental charge of
the unbroken U(1) gauge field can appear as free particles. Adding the usual CS
term for the broken U(1) gauge fields does not change much. It merely leads to
additional Aharonov-Bohm interactions among these particles. Upon introducing
the CS term for the unbroken U(1) gauge fields, in contrast, the confinement
phenomenon completely disappears.Comment: 8+2 pages, latex, no figures. References added, to appear in Phys.
Lett.
On the Absence of Cross-Confinement for Dynamically Generated Multi-Chern-Simons Theories
We show that when the induced parity breaking part of the effective action
for the low-momentum region of U(1) x ... x U(1) Maxwell gauge field theory
with massive fermions in 3 dimensions is coupled to a \phi^4 scalar field
theory, it is not possible to eliminate the screening of the long-range Coulomb
interactions and get external charges confined in the broken Higgs phase. This
result is valid for non-zero temperature as well.Comment: 7 pages, LaTe
Topological interactions in broken gauge theories
This thesis deals with planar gauge theories in which some gauge group G is
spontaneously broken to a finite subgroup H. The spectrum consists of magnetic
vortices, global H charges and dyonic combinations exhibiting topological
Aharonov-Bohm interactions. Among other things, we review the Hopf algebra D(H)
related to this residual discrete H gauge theory, which provides an unified
description of the spin, braid and fusion properties of the aforementioned
particles. The implications of adding a Chern-Simons (CS) term to these models
are also addressed. We recall that the CS actions for a compact gauge group G
are classified by the cohomology group H^4(BG,Z). For finite groups H this
classification boils down to the cohomology group H^3(H,U(1)). Thus the
different CS actions for a finite group H are given by the inequivalent
3-cocycles of H. It is argued that adding a CS action for the broken gauge
group G leads to additional topological interactions for the vortices governed
by a 3-cocycle for the residual finite gauge group H determined by a natural
homomorphism from H^4(BG,Z) to H^3(H,U(1)). Accordingly, the related Hopf
algebra D(H) is deformed into a quasi-Hopf algebra. These general
considerations are illustrated by CS theories in which the direct product of
some U(1) gauge groups is broken to a finite subgroup H. It turns out that not
all conceivable 3-cocycles for finite abelian gauge groups H can be obtained in
this way. Those that are not reached are the most interesting. A Z_2 x Z_2 x
Z_2 CS theory given by such a 3-cocycle, for instance, is dual to an ordinary
gauge theory with nonabelian gauge group the dihedral group of order eight.
Finally, the CS theories with nonabelian finite gauge group a dihedral or
double dihedral group are also discussed in full detail.Comment: 168 pages, LaTeX using amssymb.sty, 19 eps figures, all in a single
uuencoded file. PhD thesis submitted to the University of Amsterdam. Hard
copies available upon request. Postscript version also available at
http://parthe.lpthe.jussieu.fr/~mdwp
A non-abelian spin-liquid in a spin-1 quantum magnet
We study a time-reversal invariant non-abelian spin-liquid state in an symmetric spin quantum magnet on a triangular lattice. The
spin-liquid is obtained by quantum disordering a non-collinear nematic state.
We show that such a spin-liquid cannot be obtained by the standard projective
construction for spin-liquids. We also study phase transition between the
spin-liquid and the non-collinear nematic state and show that it cannot be
described within Landau-Ginzburg- Wilson paradigm.Comment: 4.25 pages, 1 figur
Non-locality of non-Abelian anyons
Topological systems, such as fractional quantum Hall liquids, promise to
successfully combat environmental decoherence while performing quantum
computation. These highly correlated systems can support non-Abelian anyonic
quasiparticles that can encode exotic entangled states. To reveal the non-local
character of these encoded states we demonstrate the violation of suitable Bell
inequalities. We provide an explicit recipe for the preparation, manipulation
and measurement of the desired correlations for a large class of topological
models. This proposal gives an operational measure of non-locality for anyonic
states and it opens up the possibility to violate the Bell inequalities in
quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure
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
Finite Group Modular Data
In a remarkable variety of contexts appears the modular data associated to
finite groups. And yet, compared to the well-understood affine algebra modular
data, the general properties of this finite group modular data has been poorly
explored. In this paper we undergo such a study. We identify some senses in
which the finite group data is similar to, and different from, the affine data.
We also consider the data arising from a cohomological twist, and write down,
explicitly in terms of quantities associated directly with the finite group,
the modular S and T matrices for a general twist, for what appears to be the
first time in print.Comment: 38 pp, latex; 5 references added, "questions" section touched-u
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