On projection (in)dependence of the dual superconductor mechanism of confinement

We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) gauge theory on the lattice. Using the Fröhlich-Marchetti monopole creation operator, we show numerically that the monopole condensate depends on the choice of the Abelian projection.     

<Emphasis Type="Italic">N</Emphasis>=1 supersymmetric conformal block recursion relations

We present explicit recursion relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 476–487, September, 2007.     

Central elements of the elliptic monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the R-matrix are studied. When the crossing parameter w takes a special rational value , where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the “quantum determinant” provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo.     

Introduction to string theory and conformal field theory

A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.     

Mirror Pairs of Quintic Orbifolds

JETP Letters - Two constructions of mirror pairs of Calabi-Yau manifolds are compared by example of quintic orbifolds $$\mathcal{Q}$$ . The first, Berglund—Hubsch—Krawitz, construction...     

Flat coordinates for Saito Frobenius manifolds and string theory

We investigate the connection between the models of topological conformal theory and noncritical string theory with Saito Frobenius manifolds. For this, we propose a new direct way to calculate the flat coordinates using the integral representation for solutions of the Gauss–Manin system connected with a given Saito Frobenius manifold. We present explicit calculations in the case of a singularity of type A _n . We also discuss a possible generalization of our proposed approach to SU(N) _k /(SU(N) _k+1 × U(1)) Kazama–Suzuki theories. We prove a theorem that the potential connected with these models is an isolated singularity, which is a condition for the Frobenius manifold structure to emerge on its deformation manifold. This fact allows using the Dijkgraaf–Verlinde–Verlinde approach to solve similar Kazama–Suzuki models.     

Anatomy of isolated monopole in Abelian projection of SU(2) lattice gauge theory

We study the structure of isolated static monopoles in the maximal Abelian projection of SU(2) lattice gluodynamics. Our estimation of the monopole radius is: R ^mon≈0.06 fm.     

Determining misorientation of graphite grains from the angular dependence of X-ray emission spectra

Angular-resolved X-ray absorption spectra were measured for pyrolytic graphite samples of various quality. A new approach to determining the misorientation of graphite grains in polycrystalline samples is proposed, which is based on calculations of the angular dependence of the relative intensity of a peak corresponding to the π* state for a normal distribution of grains. The experimental values are used to construct theoretical angular dependences using partial densities of the π* and σ* states determined from the nonempirical calculations for graphite.