Elliptic recurrence representation of the N=1 superconformal blocks in the Ramond sector

The structure of the 4-point N=1 super-conformal blocks in the Ramond sector is analyzed. The elliptic recursion relations for these blocks are derived.Comment: 21 pages, no figures. An error in the description of the R-NS block of the Ramond field and all its consequences correcte

Conformal blocks related to the R-R states in the \hat c =1 SCFT

We derive an explicit form of a family of four-point Neveu-Schwarz blocks with $\hat c =1,$ external weights $\Delta_i = 1/8$ and arbitrary intermediate weight. The derivation is based on a set of identities obeyed in the free superscalar theory by correlation functions of fields satisfying Ramond condition with respect to the bosonic (dimension 1) and the fermionic (dimension 1/2) currents.Comment: 15 pages, no figure

Elliptic recurrence representation of the N=1 Neveu-Schwarz blocks

We apply a suitably generalized method of Al. Zamolodchikov to derive an elliptic recurrence representation of the Neveu-Schwarz superconformal blocksComment: 17 pages, no figure

Modular bootstrap in Liouville field theory

The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.Comment: 11 page

Recursive representation of the torus 1-point conformal block

The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by R. Poghossian. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.Comment: 14 pages, 1 eps figure, misprints corrected and a reference adde

Recursion representation of the Neveu-Schwarz superconformal block

Four-point super-conformal blocks for the N = 1 Neveu-Schwarz algebra are defined in terms of power series of the even super-projective invariant. Coefficients of these expansions are represented both as sums over poles in the "intermediate" conformal weight and as sums over poles in the central charge of the algebra. The residua of these poles are calculated in both cases. Closed recurrence relations for the block coefficients are derived.Comment: 20 page

Limits of minimal models and continuous orbifolds

The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be equivalent to the singlet sector of a free boson theory, thus paralleling exactly the structure of the free theory in the Klebanov-Polyakov proposal. In 2d, the singlet sector does not describe a consistent theory by itself since the corresponding partition function is not modular invariant. However, it can be interpreted as the untwisted sector of a continuous orbifold, and this point of view suggests that it can be made consistent by adding in the appropriate twisted sectors. We show that these twisted sectors account for the `light states' that were not included in the original 't Hooft limit. We also show that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold agrees precisely with the limit theory of Runkel & Watts. In particular, this implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published versio

Interleukin-1beta Promoter (−31T/C and −511C/T) Polymorphisms in Major Recurrent Depression

To elucidate a genetic predisposition to major depressive disorder, we investigated two polymorphisms (−31T/C and −511C/T) in the interleukin-1beta promoter region in patients who suffered from major recurrent depression. The aim of the current work was to compare alleles and genotype layout between patients with major recurrent depression and healthy people. We would like to indicate such combination of genotypes which corresponds with major recurrent depression. Correlations between genotypes for analyzed polymorphisms and number of episodes, number of points in Hamilton Depression Rating Scale, and age of onset were investigated as well. The study group consisted of 94 patients diagnosed with major recurrent depression. The control group included 206 healthy individuals. Both groups involved representatives of Caucasian population. Genotyping of polymorphisms was performed by using PCR-RFLP technique. A specific haplotype, composed of the C allele at −31 and the T allele at −511, has a tendency to have a statistically significant difference (p = 0.064) between patients and control group. Correspondence analysis revealed that genotype T/T at −31 and genotype C/C at −511 are associated with major recurrent depression. No association was found between genotypes for studied polymorphic sites and number of episodes, number of points in Hamilton Depression Rating Scale, and age of onset