Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte

Superconducting Single-photon Detectors Made of Ultra-thin VN Films

We optimized technology of thin VN films deposition in order to study VN-based superconducting single-photon detectors. Investigation of the main VN film parameters showed that this material has lower resistivity compared to commonly used NbN. Fabricated from obtained films devices showed 100% intrinsic detection efficiency at 900 nm, at the temperature of 1.7 K starting with the bias current of 0.7·

On 3d extensions of AGT relation

An extension of the AGT relation from two to three dimensions begins from connecting the theory on domain wall between some two S-dual SYM models with the 3d Chern-Simons theory. The simplest kind of such a relation would presumably connect traces of the modular kernels in 2d conformal theory with knot invariants. Indeed, the both quantities are very similar, especially if represented as integrals of the products of quantum dilogarithm functions. However, there are also various differences, especially in the "conservation laws" for integration variables, which hold for the monodromy traces, but not for the knot invariants. We also discuss another possibility: interpretation of knot invariants as solutions to the Baxter equations for the relativistic Toda system. This implies another AGT like relation: between 3d Chern-Simons theory and the Nekrasov-Shatashvili limit of the 5d SYM.Comment: 23 page

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

Lipid Regulators during Atherogenesis : expression of LXR, PPAR, and SREBP mRNA in the Human Aorta

Transcription factors LXRs, PPARs, and SREBPs have been implicated in a multitude of physiological and pathological processes including atherogenesis. However, little is known about the regulation of these transcription factors at different stages of atherosclerosis progression. Quantitative real-time polymerase chain reaction (qRT-PCR) was used to compare the contents of mRNAs in pairs intact-injured aorta fragments taken from the same donors. Only minor changes in LXR?, LXR?, PPAR?, PPAR?, SREBP1, and SREBP2 mRNA levels were found in initial lesions as compared with intact non-diseased tissue. The contents of all mRNAs but SREBP2 mRNA were found to be progressively up-regulated in fatty streaks and fibrous lipoid plaques. These changes were only partially reproduced in cultured macrophages upon lipid loading. Wave-shaped changes in abundance of correlations between given group of mRNAs and 28 atherosclerosis-related mRNA species in the course of atherogenesis were observed. The impact of specific mRNA correlations on the total correlations also significantly varied between different lesion types. The study suggests that the extent and forms of LXR/PPAR/SREBP participation in intima functions vary nonlinear in individual fashion in atherogenesis. We speculate that the observed changes in mRNAs expression and coupling reflect shifts in lipid ligands availability and cellular composition in the course of atherosclerosis progression

Challenges of beta-deformation

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.Comment: 20 page