Single-mode approximation and effective Chern-Simons theories for quantum Hall systems

A unified description of elementary and collective excitations in quantum Hall systems is presented within the single-mode approximation (SMA) framework, with emphasis on revealing an intimate link with Chern-Simons theories. It is shown that for a wide class of quantum Hall systems the SMA in general yields, as an effective theory, a variant of the bosonic Chern-Simons theory. For single-layer systems the effective theory agrees with the standard Chern-Simons theory at long wavelengths whereas substantial deviations arise for collective excitations in bilayer systems. It is suggested, in particular, that Hall-drag experiments would be a good place to detect out-of-phase collective excitations inherent to bilayer systems. It is also shown that the intra-Landau-level modes bear a similarity in structure (though not in scale) to the inter-Landau-level modes, and its implications on the composite-fermion and composite-boson theories are discussed.Comment: 9 pages, Revtex

Electromagnetic characteristics and effective gauge theory of double-layer quantum Hall systems

The electromagnetic characteristics of double-layer quantum Hall systems are studied, with projection to the lowest Landau level taken into account and intra-Landau-level collective excitations treated in the single-mode approximation. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems. In particular, the presence of the dipole-active interlayer out-of-phase collective excitations, inherent to double-layer systems, modifies the leading O(k) and O(k^{2}) long-wavelength characteristics (i.e., the transport properties and characteristic scale) of the double-layer quantum Hall states substantially. We apply bosonization techniques and construct from such electromagnetic characteristics an effective theory, which consists of three vector fields representing the three dipole-active modes, one interlayer collective mode and two inter-Landau-level cyclotron modes. This effective theory properly incorporates the spectrum of collective excitations on the right scale of the Coulomb energy and, in addition, accommodates the favorable transport properties of the standard Chern-Simons theories.Comment: 10 pages, Revtex, sec. II slightly shortened, to appear in Phys. Rev.

Exact Solution of the one-impurity quantum Hall problem

The problem of a non-relativistic electron in the presence of a uniform electromagnetic field and of one impurity, described by means of an Aharonov-Bohm point-like vortex, is studied. The exact solution is found and the quantum Hall's conductance turns out to be the same as in the impurity-free case. This exactly solvable model seems to give indications, concerning the possible microscopic mechanisms underlying the integer quantum Hall effect, which sensibly deviate from some proposals available in the literature.Comment: 25 pages, TeX, to appear in J. Phys.

On Low-Energy Effective Actions in N = 2, 4 Superconformal Theories in Four Dimensions

We study some aspects of low-energy effective actions in 4-d superconformal gauge theories on the Coulomb branch. We describe superconformal invariants constructed in terms of N=2 abelian vector multiplet which play the role of building blocks for the N=2,4 supersymmetric low-energy effective actions. We compute the one-loop effective actions in constant N=2 field strength background in N=4 SYM theory and in N=2 SU(2) SYM theory with four hypermultiplets in fundamental representation. Using the classification of superconformal invariants we then find the manifestly N=2 superconformal form of these effective actions. While our explicit computations are done in the one-loop approximation, our conclusions about the structure of the effective actions in N=2 superconformal theories are general. We comment on some applications to supergravity - gauge theory duality in the description of D-brane interactions.Comment: 18 pages, latex, comments/reference adde

O(1/N_f) Corrections to the Thirring Model in 2<d<4

The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor conceptual changes - algebra unaffected

Bacterial artificial chromosomes as analytical basis for gene transcriptional machineries

Bacterial Artificial Chromosomes (BACs) had been minimal components of various genome-sequencing projects, constituting perfect analytical basis for functional genomics. Here we describe an enhancer screening strategy in which BAC clones that cover any genomic segments of interest are modified to harbor a reporter cassette by transposon tagging, then processed to carry selected combinations of gene regulatory modules by homologous recombination mediated systematic deletions. Such engineered BAC-reporter constructs in bacterial cells are ready for efficient transgenesis in mice to evaluate activities of gene regulatory modules intact or absent in the constructs. By utilizing the strategy, we could speedily identify a critical genomic fragment for spatio-temporally regulated expression of a mouse cadherin gene whose structure is extraordinarily huge and intricate. This BAC-based methodology would hence provide a novel screening platform for gene transcriptional machineries that dynamically fluctuate during development, pathogenesis and/or evolution

Variant supercurrents and Noether procedure

Consistent supercurrent multiplets are naturally associated with linearized off-shell supergravity models. In arXiv:1002.4932 we presented the hierarchy of such supercurrents which correspond to all the models for linearized 4D N = 1 supergravity classified a few years ago. Here we analyze the correspondence between the most general supercurrent given in arXiv:1002.4932 and the one obtained eight years ago in hep-th/0110131 using the superfield Noether procedure. We apply the Noether procedure to the general N = 1 supersymmetric nonlinear sigma-model and show that it naturally leads to the so-called S-multiplet, revitalized in arXiv:1002.2228.Comment: 6 page

On the stability of renormalizable expansions in three-dimensional gravity

Preliminary investigations are made for the stability of the $1/N$ expansion in three-dimensional gravity coupled to various matter fields, which are power-counting renormalizable. For unitary matters, a tachyonic pole appears in the spin-2 part of the leading graviton propagator, which implies the unstable flat space-time, unless the higher-derivative terms are introduced. As another possibility to avoid this spin-2 tachyon, we propose Einstein gravity coupled to non-unitary matters. It turns out that a tachyon appears in the spin-0 or -1 part for any linear gauges in this case, but it can be removed if non-minimally coupled scalars are included. We suggest an interesting model which may be stable and possess an ultraviolet fixed point.Comment: 32 pages. (A further discussion to avoid tachyons is included. To be Published in Physical Review D.

On the Background Field Method Beyond One Loop: A manifestly covariant derivative expansion in super Yang-Mills theories

There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multi-loop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in N-extended superspace.Comment: 32 pages, latex, 7 EPS figures. v2: references, comments added, typos corrected, incorrect `skeleton' conjecture in sect. 3 replaced by a more careful treatment. v3: typos corrected, final version published in JHE

One-loop effective action in N=2{\cal N}=2 supersymmetric massive Yang-Mills theory

We consider the ${\cal N}=2$ supersymmetric theory of the massive Yang-Mills field formulated in the ${\cal N}=2$ harmonic superspace. The various gauge-invariant forms of writing the mass term in the action (in particular, using the Stueckelberg superfield), which result in dual formulations of the theory, are presented. We develop a gauge-invariant and explicitly supersymmetric scheme of the loop off-shell expansion of the superfield effective action. In the framework of this scheme, we calculate gauge-invariant and explicitly ${\cal N}=2$ supersymmetric one-loop counterterms including new counterterms depending on the Stueckelberg superfield. Component structure of one of these counterterms is analyzed.Comment: 18, pages, Accepted for publication in Theor. Math. Phy