On Extensions of Superconformal Algebras

Starting from vector fields that preserve a differential form on a Riemann sphere with Grassmann variables, one can construct a Superconformal Algebra by considering central extensions of the algebra of vector fields. In this note, the N=4 case is analyzed closely, where the presence of weight zero operators in the field theory forces the introduction of non-central extensions. How this modifies the existing Field Theory, Representation Theory and Gelfand-Fuchs constructions is discussed. It is also discussed how graded Riemann sphere geometry can be used to give a geometrical description of the central charge in the N=1 theory.Comment: 16 Pages, LaTeX2e, references added, typesetting fixed, Journal ref adde

Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.Comment: 16 pages, 5 figure

Continuously Crossing u=z in the H3+ Boundary CFT

For AdS boundary conditions, we give a solution of the H3+ two point function involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the full (u,z) unit square. It consists of two patches, one for z<u and one for u<z. Along the u=z "singularity", the solutions from both patches are shown to have finite limits and are merged continuously as suggested by the work of Hosomichi and Ribault. From this two point function, we can derive b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as continuous AdS_2 branes are consistent with our novel shift equations without any new restrictions.Comment: version to appear in JHEP - 12 pages now; sign error with impact on some parts of the interpretation fixed; material added to become more self-contained; role of bulk-boundary OPE in section 4 more carefully discussed; 3 references adde

The influence of the strength of bone on the deformation of acetabular shells : a laboratory experiment in cadavers

Date of Acceptance: 24/08/2014 ©2015 The British Editorial Society of Bone & Joint Surgery. The authors would like to thank N. Taylor (3D Measurement Company) for his work with regard to data acquisition and processing of experimental data. We would also like to thank Dr A. Blain of Newcastle University for performing the statistical analysis The research was supported by the NIHR Newcastle Biomedical Research Centre. The authors P. Dold, M. Flohr and R. Preuss are employed by Ceramtec GmbH. Martin Bone received a salary from the joint fund. The author or one or more of the authors have received or will receive benefits for personal or professional use from a commercial party related directly or indirectly to the subject of this article. This article was primary edited by G. Scott and first proof edited by J. Scott.Peer reviewedPostprin

Correlation functions of disorder operators in massive ghost theories

The two-dimensional ghost systems with negative integral central charge received much attention in the last years for their role in a number of applications and in connection with logarithmic conformal field theory. We consider the free massive bosonic and fermionic ghost systems and concentrate on the non-trivial sectors containing the disorder operators. A unified analysis of the correlation functions of such operators can be performed for ghosts and ordinary complex bosons and fermions. It turns out that these correlators depend only on the statistics although the scaling dimensions of the disorder operators change when going from the ordinary to the ghost case. As known from the study of the ordinary case, the bosonic and fermionic correlation functions are the inverse of each other and are exactly expressible through the solution of a non-linear differential equation.Comment: 8 pages, late

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

Logarithmic two-point correlators in the Abelian sandpile model

We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\sigma_{1,1} \simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\sigma_{1,h} \simeq (c_h\log r + d_h)/r^4 + {\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients $c_h$ and $d_h$ (the latter are new).Comment: 28 page

Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model

We generalize the string functions C_{n,r}(tau) associated with the coset ^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau) associated with the coset W(k)/u(1) of the W-algebra of the logarithmically extended ^sl(2)_k conformal field model with positive integer k. The higher string functions occur in decomposing W(k) characters with respect to level-k theta and Appell functions and their derivatives (the characters are neither quasiperiodic nor holomorphic, and therefore cannot decompose with respect to only theta-functions). The decomposition coefficients, to be considered ``logarithmic parafermionic characters,'' are given by A_{n,r}(tau), B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra characters of the (p=k+2,1) logarithmic model. We study the properties of A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string functions C_{n,r}, and evaluate the modular group representation generated from A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular transformations of the higher-level Appell functions and the associated transcendental function Phi.Comment: 34 pages, amsart++, times. V2: references added; minor changes; some nonsense in B.3.3. correcte

Impurity intrusion in radio-frequency micro-plasma jets operated in ambient air

Space and time resolved concentrations of helium metastable atoms in an atmospheric pressure radio-frequency micro-plasma jet were measured using tunable diode laser absorption spectroscopy. Spatial profiles as well as lifetime measurements show significant influences of air entering the discharge from the front nozzle and of impurities originating from the gas supply system. Quenching of metastables was used to deduce quantitative concentrations of intruding impurities. The impurity profile along the jet axis was determined from optical emission spectroscopy as well as their dependance on the feed gas flow through the jet.Comment: Journal of Physics D: Applied Physics (accepted), 6 page

Wind on the boundary for the Abelian sandpile model

We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic orientation, and, more strangely, they cannot be imposed uniformly on a whole boundary (like the edge of a cylinder). They lead to seven new boundary condition changing fields, some of them being in highest weight representations (weights -1/8, 0 and 3/8), some others belonging to indecomposable representations with rank 2 Jordan cells (lowest weights 0 and 1). Their fusion algebra appears to be in full agreement with the fusion rules conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure