Zamalodchikov's C-Theorem and The Logarithmic Conformal Field Theory

We consider perturbation of a conformal field theory by a pair of relevant logarithmic operators and calculate the beta function up to two loops. We observe that the beta function can not be derived from a potential. Thus the renormalization group trajectories are not always along decreasing values of the central charge. However there exists a domain of structure constants in which the c-theorem still holds.Comment: 10 pages, latex, no figures, some references are added, The role of coefficients of the OPE in LCFT on the beta-functions are disscuse

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.

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

On conformal Jordan cells of finite and infinite rank

This work concerns in part the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. It is also discussed how a procedure similar to Lie algebra contractions may reduce a conformal Jordan cell of finite rank to one of lower rank. A conformal Jordan cell of rank one corresponds to a primary field. This offers a picture in which any finite conformal Jordan cell of a given conformal weight may be obtained from a universal covering cell of the same weight but infinite rank.Comment: 9 pages, LaTeX, v2: typo corrected, comments added, version to be publishe

Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference

Extended chiral algebras in the SU(2)_0 WZNW model

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly reduce to those found in c=-2. We explicitly find the free field representations for the chiral j=2 and j=3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j=2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.Comment: 18 pages LATEX. Minor corrections. Full j=2 algebra adde

Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas

We study a set of chiral symmetries contained in degenerate operators beyond the `minimal' sector of the c(p,q) models. For the operators h_{(2j+2)q-1,1}=h_{1,(2j+2)p-1} at conformal weight [ (j+1)p-1 ][ (j+1)q -1 ], for every 2j \in N, we find 2j+1 chiral operators which have quantum numbers of a spin j representation of SU(2). We give a free-field construction of these operators which makes this structure explicit and allows their OPEs to be calculated directly without any use of screening charges. The first non-trivial chiral field in this series, at j=1/2, is a fermionic or para-fermionic doublet. The three chiral bosonic fields, at j=1, generate a closed W-algebra and we calculate the vacuum character of these triplet models.Comment: 23 pages Late

Exact Two-Point Correlation Functions of Turbulence Without Pressure in Three-Dimensions

We investigate exact results of isotropic turbulence in three-dimensions when the pressure gradient is negligible. We derive exact two-point correlation functions of density in three-dimensions and show that the density-density correlator behaves as $|{x_1 - x_2}|^{-\alpha_3}$, where $\alpha_3 = 2 + \frac{\sqrt{33}}{6}$. It is shown that, in three-dimensions, the energy spectrum $E(k)$ in the inertial range scales with exponent $2 - \frac {\sqrt{33}}{12} \simeq 1.5212$. We also discuss the time scale for which our exact results are valid for strong 3D--turbulence in the presence of the pressure. We confirm our predictions by using the recent results of numerical calculations and experiment.Comment: 9 pages, latex, no figures, we have corrected the our basic equations. We predict the inertial-range exponent for the energy spectrum for 3D-turbulence without pressure. We will present the detail of calculation and the results for 2D-turbulence elsewhere. Also some references are adde

The Exact N-point Generating Function in Polyakov-Burgers Turbulence

We find the exact N-point generating function in Polyakov's approach to Burgers turbulence.Comment: 7 pages,Latex,no figure

Effect of a gap opening on the conductance of graphene superlattices

The electronic transmission and conductance of a gapped graphene superlattice were calculated by means of the transfer-matrix method. The system that we study consists of a sequence of electron-doped graphene as wells and hole-doped graphene as barriers. We show that the transmission probability approaches unity at some critical value of the gap. We also find that there is a domain around the critical gap value for which the conductance of the system attains its maximum value.Comment: 14 pages, 5 figures. To appear in Solid State Communication