Superpolynomials for toric knots from evolution induced by cut-and-join operators

The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R-matrix and ends up with a trivially-looking split W representation familiar from character calculus applications to matrix models and Hurwitz theory. Substitution of MacDonald polynomials for characters in these formulas provides a very simple description of "superpolynomials", much simpler than the recently studied alternative which deforms relation to the WZNW theory and explicitly involves the Littlewood-Richardson coefficients. A lot of explicit expressions are presented for different representations (Young diagrams), many of them new. In particular, we provide the superpolynomial P_[1]^[m,km\pm 1] for arbitrary m and k. The procedure is not restricted to the fundamental (all antisymmetric) representations and the torus knots, still in these cases some subtleties persist.Comment: 23 pages + Tables (51 pages

Optimization of a charge-state analyzer for ECRIS beams

A detailed experimental and simulation study of the extraction of a 24 keV He-ion beam from an ECR ion source and the subsequent beam transport through an analyzing magnet is presented. We find that such a slow ion beam is very sensitive to space-charge forces, but also that the neutralization of the beam's space charge by secondary electrons is virtually complete for beam currents up to at least 0.5 mA. The beam emittance directly behind the extraction system is 65 pi mm mrad and is determined by the fact that the ion beam is extracted in the strong magnetic fringe field of the ion source. The relatively large emittance of the beam and its non-paraxiality lead, in combination with a relatively small magnet gap, to significant beam losses and a five-fold increase of the effective beam emittance during its transport through the analyzing magnet. The calculated beam profile and phase-space distributions in the image plane of the analyzing magnet agree well with measurements. The kinematic and magnet aberrations have been studied using the calculated second-order transfer map of the analyzing magnet, with which we can reproduce the phase-space distributions of the ion beam behind the analyzing magnet. Using the transfer map and trajectory calculations we have worked out an aberration compensation scheme based on the addition of compensating hexapole components to the main dipole field by modifying the shape of the poles. The simulations predict that by compensating the kinematic and geometric aberrations in this way and enlarging the pole gap the overall beam transport efficiency can be increased from 16 to 45%

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the well-known Delzant construction of Hamiltonian toric manifolds. We establish the following topological properties of N: every N embeds as a submanifold in the corresponding moment-angle manifold Z, and every N is the total space of two different fibrations, one over the torus T^{m-n} with fibre a real moment-angle manifold R, and another over a quotient of R by a finite group with fibre a torus. These properties are used to produce new examples of Hamiltonian-minimal Lagrangian submanifolds with quite complicated topology.Comment: 14 pages, published version (minor changes

Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial

An elementary introduction to Khovanov construction of superpolynomials. Despite its technical complexity, this method remains the only source of a definition of superpolynomials from the first principles and therefore is important for development and testing of alternative approaches. In this first part of the review series we concentrate on the most transparent and unambiguous part of the story: the unreduced Jones superpolynomials in the fundamental representation and consider the 2-strand braids as the main example. Already for the 5_1 knot the unreduced superpolynomial contains more items than the ordinary Jones.Comment: 33 page

Bremsstrahlung analysis through the microwave cutoff and afterglow performances

Bremsstralung spectra with a very good energy resolution have been obtained for various time slabs of a few ms throughout the microwave cutoff. In a recent work (1) we had noticed+ and explained why the enhancement of the extracted high charge currents by the afterglow effect is more pronounced when the X-ray emission in the heating stage is more intense. In the present communication, we give some additional information deduced from our spectra. We indicate estimates of the temperature parameter and of the density of the hot electron population at various times. For this purpose the method presented in ref.(3) was adapted to argon. We also determine the maximum energy reached by the electrons in the steady state; the spare results seem to follow the scaling law indicated in Geller's book (4)

Bosonic topological insulator intermediate state in the superconductor-insulator transition

A low-temperature intervening metallic regime arising in the two-dimensional superconductor-insulator transition challenges our understanding of electronic fluids. Here we develop a gauge theory revealing that this emergent anomalous metal is a bosonic topological insulator where bulk transport is suppressed by mutual statistics interactions between out-of-condensate Cooper pairs and vortices and the longitudinal conductivity is mediated by symmetry-protected gapless edge modes. We explore the magnetic-field-driven superconductor-insulator transition in a niobium titanium nitride device and find marked signatures of a bosonic topological insulator behavior of the intervening regime with the saturating resistance. The observed superconductor-anomalous metal and insulator-anomalous metal dual phase transitions exhibit quantum Berezinskii-Kosterlitz-Thouless criticality in accord with the gauge theory

New matrix model solutions to the Kac-Schwarz problem

We examine the Kac-Schwarz problem of specification of point in Grassmannian in the restricted case of gap-one first-order differential Kac-Schwarz operators. While the pair of constraints satisfying $[{\cal K}_1,W] = 1$ always leads to Kontsevich type models, in the case of $[{\cal K}_1,W] = W$ the corresponding KP $\tau$-functions are represented as more sophisticated matrix integrals.Comment: 19 pages, latex, no figures, contribution to the proceedings of the 29th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, German

BPS Monopole Equation in Omega-background

We study deformed supersymmetries in N=2 super Yang-Mills theory in the Omega-backgrounds characterized by two complex parameters $\epsilon_1, \epsilon_2$. When one of the $\epsilon$-parameters vanishes, the theory has extended supersymmetries. We compute the central charge of the algebra and obtain the deformed BPS monopole equation. We examine supersymmetries preserved by the equation.Comment: 14 pages, typos corrected, published version in JHE

Generalized matrix models and AGT correspondence at all genera

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2 gauge theory as the spectral curve of the generalized matrix model, thus providing a check of AGT correspondence at all genera.Comment: 19 pages; v2: version to appear in JHE