Sigma models with AkA_k singularities in Euclidean spacetime of dimension 0<=D<4 and in the limit N->infinity

For the case of the single-O($N$)-vector linear sigma models the critical behaviour following from any $A_k$ singularity in the action is worked out in the double scaling limit $N \rightarrow \infty$, $f_r \rightarrow f_r^c$, $2 \leq r \leq k$. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for all $A_k$ and spacetime dimensions $0 \leq D < 4$. There appear exceptional spacetime dimensions where the degree $k$ of the singularity $A_k$ is more strongly constrained than by the renormalizability requirement.Comment: LaTeX, 25 pages, no figure

Double Scaling Limits, Airy Functions and Multicritical Behaviour in O(N) Vektor Sigma Models

O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N --> infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a generalized Airy function in the case of spacetime dimension zero and the partition function of a scalar field theory for positive spacetime dimension.Comment: 14 pages, LaTe

Aspects of the conformal operator product expansion in AdS/CFT correspondence

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.Comment: 31 pages, LaTeX, accepted for publication in ATM

The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.Comment: 24 pages, LaTe

Hydroxyproline-containing collagen analogs trigger the release and activation of collagen-sequestered proMMP-2 by competition with prodomain-derived peptide P33-42.

BACKGROUND: Fibrolytic and profibrotic activities of the matrix metalloproteinases (MMPs)-2 and -9 play a central role in liver fibrosis. Since binding to the extracellular matrix influences the activity of both gelatinases, here the role of fibrillar collagens as the most abundant matrix components in fibrotic tissue was investigated. RESULTS: In situ zymography and immunohistology showed association of enzymatically inactive prodomain-containing proMMP-2 and proMMP-9 but not of their activated forms to fibrillar collagen structures, which are not substrates of these gelatinases. In solid-phase binding studies with human collagens and collagen fragments, up to 45% of [125I]-labeled proMMP-2 and proMMP-9 but not of active (act)MMP-2 and actMMP-9 were retained by natural collagenous molecules and by synthetic analogs containing repeated Gly-Pro-Hyp triplets (GPO). Surface plasmon resonance yielded binding constants for the interaction of collagen type I (CI) with proMMP-2 and proMMP-9 in a nanomolar range. Values for actMMP-2 and actMMP-9 were 30-40 times higher. Tenfold molar excesses of (GPO)10 reduced the interaction of CI with pro- and actMMP-2 by 22- or 380-fold and resulted in prodomain release accompanied by high enzymatic activation and activity. Pointing to gelatine substrate displacement, higher (GPO)10 concentrations blocked the enzymatic activity. The MMP-2 prodomain-derived collagen-binding domain peptide (P33-42) binds to the collagen-binding domain of MMP-2, thereby preserving enzymatic inactivity. Synthetic P33-42 peptide competed with proMMP-2 binding to CI and prevented (GPO)10-mediated proMMP-2 activation. In contrast to (GPO)10, P33-42 did not activate proMMP-2, making triple helical and hydroxyproline-containing (GPO)10 unique in modulating gelatinase availability and activity. CONCLUSIONS: These findings suggest novel strategies using collagen analogs for the resolution of liver fibrosis via fibrotic matrix-sequestered gelatinases.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are