Bulk correlation functions in 2D quantum gravity

We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville gravity with non-rational matter central charge c<1, following and comparing two approaches. The continuous CFT approach exploits the action on the tachyons of the ground ring generators deformed by Liouville and matter ``screening charges''. A by-product general formula for the matter 3-point OPE structure constants is derived. We also consider a ``diagonal'' CFT of 2D quantum gravity, in which the degenerate fields are restricted to the diagonal of the semi-infinite Kac table. The discrete formulation of the theory is a generalization of the ADE string theories, in which the target space is the semi-infinite chain of points.Comment: 14 pages, 2 figure

The influence of indolequinoxaline, naphthalimide and benzoizatin on the growth of agrobacterium tumefaciens

The influence of indolequinoxaline, naphthalimide and benzoizatin on the growth of Agrobacterium tumefaciens on selective nutrient media was researched

Integrability in SFT and new representation of KP tau-function

We are investigating the properties of vacuum and boundary states in the CFT of free bosons under the conformal transformation. We show that transformed vacuum (boundary state) is given in terms of tau-functions of dispersionless KP (Toda) hierarchies. Applications of this approach to string field theory is considered. We recognize in Neumann coefficients the matrix of second derivatives of tau-function of dispersionless KP and identify surface states with the conformally transformed vacuum of free field theory.Comment: 25 pp, LaTeX, reference added in the Section 3.

Surface modification of polymeric materials by cold atmosphericplasma jet

In this work we report the surface modification of different engineering polymers, such as, polyethylene terephthalate (PET), polyethylene (PE) and polypropylene (PP) by an atmospheric pressure plasma jet (APPJ). It was operated with Ar gas using 10 kV, 37 kHz, sine wave as an excitation source. The aim of this study is to determine the optimal treatment conditions and also to compare the polymer surface modification induced by plasma jet with the one obtained by another atmospheric pressure plasma source the dielectric barrier discharge (DBD). The samples were exposed to the plasma jet effluent using a scanning procedure, which allowed achieving a uniform surface modification. The wettability assessments of all polymers reveal that the treatment leads to reduction of more than 40 degrees in the water contact angle (WCA). Changes in surface composition and chemical bonding were analyzed by x-ray photoelectron spectroscopy (XPS) and Fourier-Transformed Infrared spectroscopy (FTIR) that both detected incorporation of oxygen-related functional groups. Surface morphology of polymer samples was investigated by Atomic Force Microscopy (AFM) and an increase of polymer roughness after the APPJ treatment was found. The plasma-treated polymers exhibited hydrophobic recovery expressed in reduction of the O-content of the surface upon rinsing with water. This process was caused by the dissolution of low molecular weight oxidized materials (LMWOMs) formed on the surface as a result of the plasma exposure. (C) 2014 Elsevier B.V. All rights reserved

The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.Comment: 30 pages, 5 figure

Loop models, random matrices and planar algebras

We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar algebra. We apply this construction to compute the generating functions of the Potts model on a random planar map

Normal random matrix ensemble as a growth problem

In general or normal random matrix ensembles, the support of eigenvalues of large size matrices is a planar domain (or several domains) with a sharp boundary. This domain evolves under a change of parameters of the potential and of the size of matrices. The boundary of the support of eigenvalues is a real section of a complex curve. Algebro-geometrical properties of this curve encode physical properties of random matrix ensembles. This curve can be treated as a limit of a spectral curve which is canonically defined for models of finite matrices. We interpret the evolution of the eigenvalue distribution as a growth problem, and describe the growth in terms of evolution of the spectral curve. We discuss algebro-geometrical properties of the spectral curve and describe the wave functions (normalized characteristic polynomials) in terms of differentials on the curve. General formulae and emergence of the spectral curve are illustrated by three meaningful examples.Comment: 44 pages, 14 figures; contains the first part of the original file. The second part will be submitted separatel

On Associativity Equations in Dispersionless Integrable Hierarchies

We discuss the origin of the associativity (WDVV) equations in the context of quasiclassical or Whitham hierarchies. The associativity equations are shown to be encoded in the dispersionless limit of the Hirota equations for KP and Toda hierarchies. We show, therefore, that any tau-function of dispersionless KP or Toda hierarchy provides a solution to associativity equations. In general, they depend on infinitely many variables. We also discuss the particular solution to the dispersionless Toda hierarchy that describes conformal mappings and construct a family of new solutions to the WDVV equations depending on finite number of variables.Comment: 16 pages, LaTe

Minimal Superstrings and Loop Gas Models

We reformulate the matrix models of minimal superstrings as loop gas models on random surfaces. In the continuum limit, this leads to the identification of minimal superstrings with certain bosonic string theories, to all orders in the genus expansion. RR vertex operators arise as operators in a Z_2 twisted sector of the matter CFT. We show how the loop gas model implements the sum over spin structures expected from the continuum RNS formulation. Open string boundary conditions are also more transparent in this language.Comment: 36 pages, 3 figure