Difficulties of an Infrared Extension of Differential Renormalization

We investigate the possibility of generalizing differential renormalization of D.Z.Freedman, K.Johnson and J.I.Latorre in an invariant fashion to theories with infrared divergencies via an infrared $\tilde{R}$ operation. Two-dimensional $\sigma$ models and the four-dimensional $\phi^4$ theory diagrams with exceptional momenta are used as examples, while dimensional renormalization serves as a test scheme for comparison. We write the basic differential identities of the method simultaneously in co-ordinate and momentum space, introducing two scales which remove ultraviolet and infrared singularities. The consistent set of Fourier-transformation formulae is derived. However, the values for tadpole-type Feynman integrals in higher orders of perturbation theory prove to be ambiguous, depending on the order of evaluation of the subgraphs. In two dimensions, even earlier than this ambiguity manifests itself, renormalization-group calculations based on infrared extension of differential renormalization lead to incorrect results. We conclude that the extended differential renormalization procedure does not perform the infrared $\tilde{R}$ operation in a self-consistent way, as the original recipe does the ultraviolet $R$ operation.Comment: (minor changes have been made to make clear that no infrared problems occur in the original ultraviolet procedure of [1]; subsection 2.1 has been added to outline the ideas a simple example), 26 pages, LaTeX, JINR preprint E2-92-538, Dubna (Dec.1992

Algebraic Curve for the SO(6) sector of AdS/CFT

We construct the general algebraic curve of degree four solving the classical sigma model on RxS5. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N=4 SYM, also constructed here. We explicitly reproduce some particular solutions

Complex Curve of the Two Matrix Model and its Tau-function

We study the hermitean and normal two matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex curve, different from the hyperelliptic curve of the one matrix model. The matrix model quantities are expressed through the periods of meromorphic generating differential on this curve and the partition function of the multiple support solution, as a function of filling numbers and coefficients of the matrix potential, is shown to be the quasiclassical tau-function. The relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multimatrix models with tree-like interactions is considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of J.Phys. A on Random Matrix Theor

Long-lived Charginos in the Focus-point Region of the MSSM Parameter Space

We analyse the possibility to get light long-lived charginos within the framework of the MSSM with gravity mediated SUSY breaking. We find out that this possibility can be realized in the so-called focus-point region of parameter space. The mass degeneracy of higgsino-like chargino and two higgsino-like neutralinos is the necessary condition for a long lifetime. It requires the fine-tuning of parameters, but being a single additional constraint in the whole parameter space it can be fulfilled in the Constrained MSSM along the border line where radiative electroweak symmetry breaking fails. In a narrow band close to the border line the charginos are long-lived particles. The cross-sections of their production and co-production at the LHC via electroweak interaction reach a few tenth of pb.Comment: LaTeX, 11 pages, 11 eps figure

Influence of carbon substitution on the heat transport in single crystalline MgB2

We report data on the thermal conductivity \kappa(T,H) in the basal plane of hexagonal single-crystalline and superconducting Mg(B_{1-x}C_x)_2 (x= 0.03, 0.06) at temperatures between 0.5 and 50 K, and in external magnetic fields H between 0 and 50 kOe. The substitution of carbon for boron leads to a considerable reduction of the electronic heat transport, while the phonon thermal conductivity seems to be much less sensitive to impurities. The introduction of carbon enhances mostly the intraband scattering in the \sigma-band. In contrast to the previously observed anomalous behavior of pure MgB$_2$, the Wiedemann-Franz law is valid for Mg(B_0.94 C_0.06)_2 at low temperatures.Comment: 4 pages, 4 figures. Final version to appear in Phys. Rev.