Fractional Quantum Hall Effect from Anomalies in WZNW Model

An approach to understand Fractional Quantum Hall Effect (FQHE) using anomalies is studied in this paper. More specifically, this is done by looking at the anomaly in the current conservation equation of a WZNW theory describing fields living at the edge of the two dimensional Hall sample. This WZNW theory itself comes from the non-Abelian bosonisation of fermions living at the edge. It is shown that this model can describe both integer and fractional quantization of conductivities in a unified manner.Comment: 14 pages, SU-4240-56

The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

We have observed the production of strings (disclination lines and loops) via the Kibble mechanism of domain (bubble) formation in the isotropic to nematic phase transition of a sample of uniaxial nematic liquid crystal. The probablity of string formation per bubble is measured to be $0.33 \pm 0.01$. This is in good agreement with the theoretical value $1/ \pi$ expected in two dimensions for the order parameter space $S^2/{\bf Z}_2$ of a simple uniaxial nematic liquid crystal.Comment: 17 pages, in TEX, 2 figures (not included, available on request

Edge States in Gauge Theories: Theory, Interpretations and Predictions

Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the dimensionality of spacetime. The intimate connection of these observables to charge fractionation, vertex operators and topological field theories is described. The edge observables, however, may or may not exist as well-defined operators in a fully quantized theory depending on the boundary conditions imposed on the fields and their momenta. The latter are obtained by requiring the Hamiltonian of the theory to be self-adjoint and positive definite. We show that these boundary conditions can also have nice physical interpretations in terms of certain experimental parameters such as the penetration depth of the electromagnetic field in a surrounding superconducting medium. The dependence of the spectrum on one such parameter is explicitly exhibited for the Higgs model on a spatial disc in its London limit. It should be possible to test such dependences experimentally, the above Higgs model for example being a model for a superconductor. Boundary conditions for the 3+1 dimensional $BF$ system confined to a spatial ball are studied. Their physical meaning is clarified and their influence on the edge states of this system (known to exist under certain conditions) is discussed. It is pointed out that edge states occur for topological solitons of gauge theories such as the 't Hooft-Polyakov monopoles.Comment: 36 pages, LATEX File (revised because figures had problems

Edge States and Entanglement Entropy

It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular, we show that the entanglement entropy of the ground state for the quantum Hall effect on a disk exhibits an approximate ``area " law.Comment: 16 pages, minor corrections and futher details adde

Cracks Cleave Crystals

The problem of finding what direction cracks should move is not completely solved. A commonly accepted way to predict crack directions is by computing the density of elastic potential energy stored well away from the crack tip, and finding a direction of crack motion to maximize the consumption of this energy. I provide here a specific case where this rule fails. The example is of a crack in a crystal. It fractures along a crystal plane, rather than in the direction normally predicted to release the most energy. Thus, a correct equation of motion for brittle cracks must take into account both energy flows that are described in conventional continuum theories and details of the environment near the tip that are not.Comment: 6 page