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

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

Off-shell superconformal nonlinear sigma-models in three dimensions

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.Comment: 67 pages; V2: typos corrected, one reference added, version to appear on JHE

Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic