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.

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

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

Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions

The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of stationary state forced KPZ equation in 1+1--dimensions. It is proved that the moments of height increments $C_a =$ behave as $|x_1 -x_2|^{\xi_a}$ with $\xi_a = a$ for length scales $|x_1-x_2| << \sigma$. The length scale $\sigma$ is the characteristic length of the forcing term. We have checked the analytical results by direct numerical simulation.Comment: 13 pages, 9 figure

Long range correlation in cosmic microwave background radiation

We investigate the statistical anisotropy and Gaussianity of temperature fluctuations of Cosmic Microwave Background radiation (CMB) data from {\it Wilkinson Microwave Anisotropy Probe} survey, using the multifractal detrended fluctuation analysis, rescaled range and scaled windowed variance methods. The multifractal detrended fluctuation analysis shows that CMB fluctuations has a long range correlation function with a multifractal behavior. By comparing the shuffled and surrogate series of CMB data, we conclude that the multifractality nature of temperature fluctuation of CMB is mainly due to the long-range correlations and the map is consistent with a Gaussian distribution.Comment: 10 pages, 7 figures, V2: Added comments, references and major correction

Macrophage Ontogeny Underlies Differences in Tumor-Specific Education in Brain Malignancies.

Extensive transcriptional and ontogenetic diversity exists among normal tissue-resident macrophages, with unique transcriptional profiles endowing the cells with tissue-specific functions. However, it is unknown whether the origins of different macrophage populations affect their roles in malignancy. Given potential artifacts associated with irradiation-based lineage tracing, it remains unclear if bone-marrow-derived macrophages (BMDMs) are present in tumors of the brain, a tissue with no homeostatic involvement of BMDMs. Here, we employed multiple models of murine brain malignancy and genetic lineage tracing to demonstrate that BMDMs are abundant in primary and metastatic brain tumors. Our data indicate that distinct transcriptional networks in brain-resident microglia and recruited BMDMs are associated with tumor-mediated education yet are also influenced by chromatin landscapes established before tumor initiation. Furthermore, we demonstrate that microglia specifically repress Itga4 (CD49D), enabling its utility as a discriminatory marker between microglia and BMDMs in primary and metastatic disease in mouse and human

Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.Comment: 10 pages, 12 figures, additional references adde