Renormalization Group Treatment of Nonrenormalizable Interactions

The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. Explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the na\"ive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms.Comment: LaTex, 11 page

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

On the notion of potential in quantum gravity

The problem of consistent definition of the quantum corrected gravitational field is considered in the framework of the $S$-matrix method. Gauge dependence of the one-particle-reducible part of the two-scalar-particle scattering amplitude, with the help of which the potential is usually defined, is investigated at the one-loop approximation. The $1/r^2$-terms in the potential, which are of zero order in the Planck constant $\hbar,$ are shown to be independent of the gauge parameter weighting the gauge condition in the action. However, the $1/r^3$-terms, proportional to $\hbar,$ describing the first proper quantum correction, are proved to be gauge-dependent. With the help of the Slavnov identities, their dependence on the weighting parameter is calculated explicitly. The reason the gauge dependence originates from is briefly discussed.Comment: LaTex 2.09, 16 pages, 5 ps figure

Phenomenology of the 1/Nf_f Expansion for Field Theories in Extra Dimensions

In this paper we review the properties of the 1/$N_f$ expansion in multidimensional theories. Contrary to the usual perturbative expansion it is renormalizable and contains only logarithmic divergencies. The price for it is the presence of ghost states which, however, in certain cases do not contribute to physical amplitudes. In this case the theory is unitary and one can calculate the cross-sections. As an example we consider the differential cross section of elastic $eq \to eq$ scattering in $D=7,11,...$-dimensional world. We look also for the unification of the gauge couplings in multidimensional Standard Model and its SUSY extension which takes place at energies lower than in 4 dimensions.Comment: Submitted for the SUSY07 proceedings, 4 pages, LaTeX, 4 eps figures + 3 axodraw figure

Manifestations of fine features of the density of states in the transport properties of KOs2O6

We performed high-pressure transport measurements on high-quality single crystals of KOs2O6, a beta-pyrochlore superconductor. While the resistivity at high temperatures might approach saturation, there is no sign of saturation at low temperatures, down to the superconducting phase. The anomalous resistivity is accompanied by a nonmetallic behavior in the thermoelectric power (TEP) up to temperatures of at least 700 K, which also exhibits a broad hump with a maximum at 60 K. The pressure influences mostly the low-energy electronic excitations. A simple band model based on enhanced density of states in a narrow window around the Fermi energy (EF) explains the main features of this unconventional behavior in the transport coefficients and its evolution under pressure

Computations in Large N Matrix Mechanics

The algebraic formulation of Large N matrix mechanics recently developed by Halpern and Schwartz leads to a practical method of numerical computation for both action and Hamiltonian problems. The new technique posits a boundary condition on the planar connected parts X_w, namely that they should decrease rapidly with increasing order. This leads to algebraic/variational schemes of computation which show remarkably rapid convergence in numerical tests on some many- matrix models. The method allows the calculation of all moments of the ground state, in a sequence of approximations, and excited states can be determined as well. There are two unexpected findings: a large d expansion and a new selection rule for certain types of interaction.Comment: 27 page

Gauge and parametrization dependence in higher derivative quantum gravity

The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the help of the generalized renormgroup method demonstrating consistency of the results obtained.Comment: 22 pages, Latex, no figure

Magnetic field dependence of the oxygen isotope effect on the magnetic penetration depth in hole-doped cuprate superconductors

The magnetic field dependence of the oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic field penetration depth \lambda_{ab} was studied in the hole-doped high-temperature cuprate superconductors YBa_2Cu_4O_8, Y_0.8Pr_0.2Ba_2Cu_3O_7-\delta, and Y_0.7Pr_0.3Ba_2Cu_3O_7-\delta. It was found that \lambda_ab for the ^{16}O substituted samples increases stronger with increasing magnetic field than for the ^{18}O ones. The OIE on \lambda_ab decreases by more than a factor of two with increasing magnetic field from \mu_0H=0.2 T to \mu_0H=0.6 T. This effect can be explained by the isotope dependence of the in-plane charge carrier mass m^\ast_{ab}.Comment: 4 pages, two figure