Duality and Non-linear Response for Quantum Hall Systems

We derive the implications of particle-vortex duality for the electromagnetic response of Quantum Hall systems beyond the linear-response regime. This provides a first theoretical explanation of the remarkable duality which has been observed in the nonlinear regime for the electromagnetic response of Quantum Hall systems.Comment: 7 pages, 1 figure, typeset in LaTe

Small and beautiful? The programme of activities and the least developed countries

Most carbon abatement projects under the Kyoto Protocol's Clean Development Mechanism (CDM) have been implemented in rapidly industrializing countries, notably China and India. To support small carbon abatement projects and to promote decarbonization in the least developed countries, the Programme of Activities (PoA) modality was introduced. Are the determinants of project implementation different under the PoA from those of conventional CDM projects? To answer this question, we conduct a statistical analysis of the global distribution of CDM projects and PoAs during the years 2007–2012. In regard to country size, large countries clearly dominate both the CDM and PoA, suggesting that the PoA may do only little to facilitate project implementation in small countries. However, the number of PoAs has a strong negative association with a country's corruption level, while the importance of corruption for the CDM is much smaller. Moreover, per capita income has no effect on PoA implementation, while high wealth levels have a weak positive effect on CDM projects. Thus, the PoA modality seems to promote sustainable development in poor countries that have exceeded a certain threshold of good governance. In this regard, PoAs are directing carbon credits to new areas, as many had initially hoped

Noticer vedkommende Agerdyrkningsvæsenet og Landboforholdene i Territoriet Wiscounsin i Nord-Amerika.

Noticer vedkommende Agerdyrkningsvæsenet og Landboforholdene i Territoriet Wiscounsin i Nord-Amerika

Derivation of the Semi-circle Law from the Law of Corresponding States

We show that, for the transition between any two quantum Hall states, the semi-circle law and the existence of a duality symmetry follow solely from the consistency of the law of corresponding states with the two-dimensional scaling flow. This puts these two effects on a sound theoretical footing, implying that both should hold exactly at zero temperature, independently of the details of the microscopic electron dynamics. This derivation also shows how the experimental evidence favours taking the two-dimensional flow seriously for the whole transition, and not just near the critical points.Comment: 4 pages, 1 figure, typeset in LaTeX (uses revtex

Duality in the Quantum Hall Effect - the Role of Electron Spin

At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of Kramers-Wannier duality for the two dimensional Ising model. The duality group, which is a subgroup of the modular group, is analysed and it is argued that there is a quantitative difference between a situation in which the spin splitting of electron energy levels is comparable to the cyclotron energy and one in which the spin splitting is much less than the cyclotron energy. In the former case the group of symmetries is larger than in the latter case. These duality symmetries are used to constrain the scaling functions of the theory and, under an assumption of complex meromorphicity, a unique functional form is obtained for the crossover of the conductivities between Hall states as a function of the external magnetic field. This analytic form is shown to give good agreement with experimental data. The analysis requires a consideration of the way in which longitudinal resistivities are extracted from the experimentally measured longitudinal resistances and a novel method is proposed for determining the correct normalisation for the former.Comment: 22 pages, 8 figures, typeset in LaTe

RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non-perturbative identity relating the $u$-modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c-theorem for N=2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References added. Version published in PR

D-Branes on K3-Fibrations

B-type D-branes are constructed on two different K3-fibrations over IP_1 using boundary conformal field theory at the rational Gepner points of these models. The microscopic CFT charges are compared with the Ramond charges of D-branes wrapped on holomorphic cycles of the corresponding Calabi-Yau manifold. We study in particular D4-branes and bundles localized on the K3 fibers, and find from CFT that each irreducible component of a bundle on K3 gains one modulus upon fibration over IP_1. This is in agreement with expectations and so provides a further test of the boundary CFT.Comment: 16p, harvmac, tables.tex; typos corrected, refs added, discussion about moduli spaces improve

Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions

A model consisting of a single massless scalar field with a topological coupling to a pure gauge field is defined and studied. It possesses an SL(2,Z) symmetry as a consequence of the gauge invariance. We propose that by adding impurities the model can be used to describe transitions between Quantum Hall plateaux. This leads to a correlation length exponent of 20/9, in excellent agreement with the most recent experimental measurements.Comment: 25 pages, minor changes in data discussion, Section V on connection with staircase model is expanded References added. Interpretive comments added in section 3 about the critical condition. with improved terminolog

Electromagnetic Response and Approximate SO(5) Symmetry in High-Tc Superconductors

It has been proposed that the effective Hamiltonian describing high T_c superconductivity in cuprate materials has an approximate SO(5) symmetry relating the superconducting (SC) and antiferromagnetic (AF) phases of these systems. We show that robust consequences of this proposal are potentially large optical conductivities and Raman scattering rates in the AF phase, due to the electromagnetic response of the doubly-charged pseudo Goldstone bosons which must exist there. This provides strong constraints on the properties of the bosons, such as their mass gap and velocity.Comment: 4 pages, 3 figure

Generalized Calabi-Yau Manifolds and the Mirror of a Rigid Manifold

We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories with $c=9$ and so are perfectly good for compactifying the heterotic string to the four dimensions of space-time. As a check of mirror symmetry we compute the structure of the space of complex structures of the mirror and check that this reproduces the known results for the Yukawa couplings and metric appropriate to the Kahler class parameters on the Z orbifold together with their instanton corrections.Comment: 39 pages, plain Te