The Logarithmic Conformal Field Theories

We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any $n$-- point function containing the logarithmic field in terms of ordinary $n$--point functions. At last, we calculate the operator product expansion (OPE) coefficients of a logarithmic conformal field theory, and show that these can be obtained from the corresponding coefficients of ordinary conformal theory by a simple derivation.Comment: 17 pages ,latex , some minor changes, to appear in Nucl. Phys.

Global Conformal Invariance in D-dimensions and Logarithmic Correlation Functions

We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation procedure, one can obtain n-point function of logarithmic field theory from those of ordinary conformal field theory.Comment: 9 pages, LaTeX, some misprints are corrected, to be published in Phys. Lett.

Logarithmic N=1 superconformal field theories

We study the logarithmic superconformal field theories. Explicitly, the two-point functions of N=1 logarithmic superconformal field theories (LSCFT) when the Jordan blocks are two (or more) dimensional, and when there are one (or more) Jordan block(s) have been obtained. Using the well known three-point fuctions of N=1 superconformal field theory (SCFT), three-point functions of N=1 LSCFT are obtained. The general form of N=1 SCFT's four-point functions is also obtained, from which one can easily calculate four-point functions in N=1 LSCFT.Comment: 10 pages, LaTeX file, minor revisions made, to appear in Phys. Lett.

Logarithmic Correlation Functions in Two Dimensional Turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the persence of three dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory $c_{8,1}$ describes the 2D- turbulence both in the absence and the presence of the perturbation. We obtain the following energy spectrum $E(k) \sim k^{-5.125 } \ln(k )$ for perturbed 2D - turbulence and $E(k) \sim k^{-5 } \ln(k )$ for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.Comment: 14 pages ,latex , no figure

Quenched Averaged Correlation Functions of the Random Magnets

It is shown that the ratios of the quenched averaged three and four-point correlation functions of the local energy density operator to the connected ones in the random-bond Ising model approach asymptotically to some $universal$ functions. We derive the explicit expressions of these universal functions. Moreover it is shown that the individual logarithmic operators have not any contribution to the connected correlation functions of the disordered Ising model.Comment: 4 pages, twocolumn, to appear in Nucl. Physics

A Logarithmic Conformal Field Theory Solution For Two Dimensional Magnetohydrodynamics In Presence of The Alf'ven Effect

When Alf`ven effect is peresent in magnetohydrodynamics one is naturally lead to consider conformal field theories, which have logarithmic terms in their correlation functions. We discuss the implications of such logarithmic terms and find a unique conformal field theory with centeral charge $c=-\frac{209}{7}$, within the border of the minimal series, which satisfies all the constraints. The energy espectrum is found to be \newline $E(k)\sim k^{-\frac{13}{7}} \log{k}$.Comment: Latex, 9 page

Variation in Fatty Acid Composition of Four Turkish Registered Poppy (Papaver somniferum L.) Seeds in two Locations (Ankara and Boldavin) of Turkey

Opium poppy (Papaver somniferum L.) has two major products: alkaloids in the capsules and the seeds. Poppy seed oil is a rich source of polyunsaturated fatty acids. It is known that polyunsaturated fatty acids present not only basic nutriments for human body, but protects against cardiovascular diseases, heart attacks and many inflammatory diseases. The aim of this study was to determine oil content and fatty acids composition in four Turkish registered poppy cultivars grown in experimental fields of the the Agronomy Department, of Ankara University and Bolvadin Factory of Alcaloids at the Afyon province, Turkey. All seeds were sown in 15 October 2009 and harvested in 20 July 2010. The oil was extracted and analysed with hexane by foss soxtec 2055 apparatus and fatty acids were analyzed by gas chromatography. Seed oil and fatty acids percentage of four different cultivars in two locations were determined. Oil contents of seed varieties ranged 40.20% - 47.95%. The major fatty acid in seed oils was linoleic acid (68.16 - 74.15%) whereas oleic and palmitic acid contents of seed oils ranged 14.22 - 16.47% and 7.96 - 12.87% respectively. In terms of oil content and unsaturated fatty acids concentration Bolvadin location is better compared to Ankara location

Boundary states in boundary logarithmic CFT

There exist logarithmic CFTs(LCFTs) such as the $c_{p,1}$ models. It is also well known that it generally contains Jordan cell structure. In this paper, we obtain the boundary Ishibashi state for a rank-2 Jordan cell structure and, with these states in $c=-2$ rational LCFT, we derive boundary states in the closed string picture, which correspond to boundary conditions in the open string picture. We also discuss the Verlinde formula for LCFT and possible applications to string theory.Comment: LaTeX, 21 pages; a reference adde

A Local Logarithmic Conformal Field Theory

The local logarithmic conformal field theory corresponding to the triplet algebra at c=-2 is constructed. The constraints of locality and crossing symmetry are explored in detail, and a consistent set of amplitudes is found. The spectrum of the corresponding theory is determined, and it is found to be modular invariant. This provides the first construction of a non-chiral rational logarithmic conformal field theory, establishing that such models can indeed define bona fide conformal field theories.Comment: 29 pages, LaTeX, minor changes, reference adde

Minimal String Theory is Logarithmic

We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity (Liouville field theory). In the Liouville sector, we show that four-point correlation functions of `tachyons' exhibit logarithmic singularities, and that the theory turns out to be logarithmic. The relation with Zamolodchikov's logarithmic degenerate fields is also discussed. Our result holds for generic values of (p,q).Comment: Latex2e 13 pages; v.2: minor corrections, typos fixe