Quantum Hall Smectics, Sliding Symmetry and the Renormalization Group

In this paper we discuss the implication of the existence of a sliding symmetry, equivalent to the absence of a shear modulus, on the low-energy theory of the quantum hall smectic (QHS) state. We show, through renormalization group calculations, that such a symmetry causes the naive continuum approximation in the direction perpendicular to the stripes to break down through infrared divergent contributions originating from naively irrelevant operators. In particular, we show that the correct fixed point has the form of an array of sliding Luttinger liquids which is free from superficially "irrelevant operators". Similar considerations apply to all theories with sliding symmetries.Comment: 7 pages, 3 figure

Functional integral over velocities for a spinning particle with and without anomalous magnetic moment in a constant electromagnetic field

The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for the particle in a constant electromagnetic field. As a by-product, we also obtain a Schwinger representation for the first case.Comment: latex, 19 page

Evidence for the PSL(2∣|2) Wess-Zumino-Novikov-Witten model as a model for the plateau transition in Quantum Hall effect: Evaluation of numerical simulations

In this paper I revise arguments in favour of the PSL(2$|$2) Wess-Zumino-Novikov-Witten (WZNW) model as a theory of the plateau transition in Integer Quantum Hall effect. I show that all available numerical data (including the correlation length exponent $\nu$) are consistent with the predictions of such WZNW model with the level $k=8$.Comment: 11 pages, no figure

Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields

The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schr\"odinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is demonstrated that aside from the known cases (a constant and uniform magnetic field that is parallel to the Aharonov-Bohm solenoid, a static spherically symmetrical electric field, and the field of a magnetic monopole), there are broad classes of additional fields. Among these new additional fields we have physically interesting electric fields acting during a finite time, or localized in a restricted region of space. There are additional time-dependent uniform and isotropic electric fields that allow exact solutions of the Schrodinger equation. In the relativistic case there are additional electric fields propagating along the Aharonov-Bohm solenoid with arbitrary electric pulse shape

Spin-1 chain with spin-1/2 excitations in the bulk

We present a spin-1 chain with a Hamiltonian which has three exactly solvable ground states. Two of these are fully dimerized, analogous to the Majumdar-Ghosh (MG) states of a spin-1/2 chain, while the third is of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type. We use variational and numerical methods to study the low-energy excitations which interpolate between these ground states in different ways. In particular, there is a spin-1/2 excitation which interpolates between the MG and AKLT ground states; this is the lowest excitation of the system and it has a surprisingly small gap. We discuss generalizations of our model of spin fractionalization to higher spin chains and higher dimensions.Comment: 7 pages including 4 figures; this is the published version of the pape

Effective action in a higher-spin background

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.Comment: 40 pages, Some errors and typos corrected, Version published in JHE

Path integral and pseudoclassical action for spinning particle in external electromagnetic and torsion fields

Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a pseudoclassical action for a spinning particle. It is just a generalization of Berezin-Marinov action to the background under consideration. Pseudoclassical equations of motion in the nonrelativistic limit reproduce exactly the classical limit of the Pauli quantum mechanics in the same case. Quantization of the action appears to be nontrivial due to an ordering problem, which needs to be solved to construct operators of first-class constraints, and to select the physical sector. Finally the quantization reproduces the Dirac equation in the given background and, thus, justifies the interpretation of the action.Comment: 18 pages, LaTeX. Small modifications, some references added. To be published in International Journal of Modern Physics

Irreducible antifield-BRST approach to reducible gauge theories

An irreducible antifield BRST quantization method for reducible gauge theories is proposed. The general formalism is illustrated in the case of the Freedman-Townsend model.Comment: 19 pages, LaTeX 2.0

Magnetization plateaus of SrCu_2(BO_3)_2 from a Chern-Simons theory

The antiferromagnetic Heisenberg model on the frustrated Shastry-Sutherland lattice is studied by a mapping onto spinless fermions carrying one quantum of statistical flux. Using a mean-field approximation these fermions populate the bands of a generalized Hofstadter problem. Their filling leads to the magnetization curve. For SrCu_2(BO_3)_2 we reproduce plateaus at 1/3 and 1/4 of the saturation moment and predict a new one at 1/2. Gaussian fluctuations are shown to be massive at these plateau values.Comment: 4 pages, 5 figure

Vacuum properties of a Non-Local Thirring-Like Model

We use path-integral methods to analyze the vacuum properties of a recently proposed extension of the Thirring model in which the interaction between fermionic currents is non-local. We calculate the exact ground state wave functional of the model for any bilocal potential, and also study its long-distance behavior. We show that the ground state wave functional has a general factored Jastrow form. We also find that it posess an interesting symmetry involving the interchange of density-density and current-current interactions.Comment: 25 pages, latex, no figure