Five-Dimensional Supersymmetric Yang-Mills Theories and Random Plane Partitions

Five-dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills theories are investigated from the viewpoint of random plane partitions. It is shown that random plane partitions are factorizable as q-deformed random partitions so that they admit the interpretations as five-dimensional Yang-Mills and as topological string amplitudes. In particular, they lead to the exact partition functions of five-dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills with the Chern-Simons terms. We further show that some specific partitions, which we call the ground partitions, describe the perturbative regime of the gauge theories. We also argue their role in string theory. The gauge instantons give the deformation of the ground partition.Comment: 33 pages, 9 figures, typos correcte

Synthesis and physical properties of (Pb0.5M0.5)(Sr,La)2CuOz (z~5; M = Fe, Co, Cu, and Zn)

(Pb0.5Cu0.5)(Sr0.5La0.5)2CuOz (abbreviated as (Pb,Cu)-"1-2-0-1") with superconducting transition temperature (Tc) of 25 K is a member (n = 1) of one of the homologous series of cuprate superconductors, (Pb4+,Cu2+)(Sr2+,Ln3+)2(Y3+,Ca2+)n-1Cu2+nO2-2n+3 (n = 1-4; Ln: lanthanoid elements). For the (Pb,Cu)-"1-2-0-1", substitution effects of 3d transition metal elements M (M = Fe, Co, and Zn) for the Cu site in the (Pb,Cu)-O charge-reservoir layer (labelled as Cu(1)) are systematically investigated. Because Fe, Co and Ni ions exist as divalent or trivalent in ionic crystals, the Sr2+/La3+ ratio in the (Sr,Ln) site is adjusted to satisfy charge neutrality, assuming that they are in a trivalent state. This results in the successful synthesis of new materials with nominal compositions of (Pb0.5M0.5)(Sr0.75La0.25)2CuOz (M = Fe and Co). This observation suggests that Fe and Co are trivalent in "1-2-0-1". For M = Zn, the nominal composition of (Pb0.5Zn0.5)(Sr0.5La0.5)2CuOz was found to yield a nearly single "1-2-0-1" phase. Temperature dependence of electrical resistivity and magnetization were measured, and superconductivity was confirmed only for the case of M = Zn with a Tc of 19.7 K. For these three materials, the distribution of Fe, Co and Zn between Cu(1) and another Cu site in the Cu-O2 plane labelled as Cu(2) was investigated employing transmission electron microscopy, which showed that Fe, Co, and Zn occupy both the Cu(1) and Cu(2) sites.Comment: 26 pages, 10 figure

Free Fermion and Seiberg-Witten Differential in Random Plane Partitions

A model of random plane partitions which describes five-dimensional $\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills is studied. We compute the wave functions of fermions in this statistical model and investigate their thermodynamic limits or the semi-classical behaviors. These become of the WKB type at the thermodynamic limit. When the fermions are located at the main diagonal of the plane partition, their semi-classical wave functions are obtained in a universal form. We further show that by taking the four-dimensional limit the semi-classical wave functions turn to live on the Seiberg-Witten curve and that the classical action becomes precisely the integral of the Seiberg-Witten differential. When the fermions are located away from the main diagonal, the semi-classical wave functions depend on another continuous parameter. It is argued that they are related with the wave functions at the main diagonal by the renormalization group flow of the underlying gauge theory.Comment: 32 pages, 3 figures, typos correcte

Gravitational Quantum Foam and Supersymmetric Gauge Theories

We study K\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of an infinite number of gravitational quanta. We count these quanta in a relative manner by measuring a deviation of the local geometry from a singular Calabi-Yau threefold, that is a A_{N-1} singularity fibred over \mathbb{P}^1. With such a regularization prescription, the number of the gravitational quanta becomes finite and turns to be the perturbative prepotential for five-dimensional \mathcal{N}=1 supersymmetric SU(N) Yang-Mills. These quanta are labelled by lattice points in a certain convex polyhedron on \mathbb{R}^3. The polyhedron becomes obtainable from a plane partition which is the ground state of a statistical model of random plane partition that describes the exact partition function for the gauge theory. Each gravitational quantum of the local geometry is shown to consist of N unit cubes of plane partitions.Comment: 43 pages, 12 figures: V2 typos correcte

Correction of Anophthalmic Enophthalmos with a Three-Staged Procedure: Two Case Reports

Surgical correction of an anophthalmic enophthalmos secondary to inappropriate repair of the eye socket involves several difficult aesthetic issues associated with long-term use of a poorly fitting prosthetic eye. In this paper, we present two cases of anophthalmic enophthalmos. During the treatment of the first patient, unsatisfactory cosmetic problems including lower eyelid retraction, hypoglobus, and severe upper eyelid ptosis were revealed. Accordingly, a three-staged procedure was performed on the second patient, including autologous augmentation of the eye socket, correction of lower eyelid retraction with a cartilage graft, and a frontalis sling procedure to correct upper eyelid ptosis

Fabrication of Bi2212 Cross Whiskers Junction

An intrinsic Josephson junction has been successfully fabricated without any micro-fabrication technique. Two Bi2212 whiskers were crossed with one another and joined by post-annealing. The inter-whisker electrical transport properties were measured by the four-probe method. The temperature dependence of resistance exhibited metallic behavior above TC. The resistance decreased to zero around 80K, corresponding to the superconducting transition. The current-voltage characteristics at 5K exhibited a small hysteresis and voltage jump, which can be explained by the intrinsic Josephson effect.Comment: 3 page PDF fil

A Cross-Whiskers Junction as a Novel Fabrication Process for Intrinsic Josephson Junction

A Bi2Sr2CaCu2O8+d cross-whiskers junction has been successfully discovered as a novel intrinsic Josephson junction without using any technique for micro-fabrication. Two Bi2Sr2CaCu2O8+d whisker crystals were placed crosswise on a MgO substrate and heated at 850C for 30 min. They were electrically connected at their c-planes. The measurement terminals were made at the four ends of the whiskers. The I-V characteristics of the cross-whiskers junction at 5K were found to show a clear multiple-branch structure with a spacing of approximately 15 mV that is a feature of the intrinsic Josephson junction. The critical current density Jc was estimated to be 1170 A/cm2. The branch-structure was strongly suppressed by the magnetic field above 1kOe.Comment: 4 pages, PDF fil

1/R gravity and Scalar-Tensor Gravity

We point out that extended gravity theories, the Lagrangian of which is an arbitrary function of scalar curvature $R$, are equivalent to a class of the scalar tensor theories of gravity. The corresponding gravity theory is $\omega=0$ Brans-Dicke gravity with a potential for the Brans-Dicke scalar field, which is not compatible with solar system experiments if the field is very light: the case when such modifications are important recently.Comment: 4 pages, to appear in PL