Lectures on Mirror Symmetry

We give an introduction to mirror symmetry of strings on Calabi-Yau manifolds with an emphasis on its applications e.g. for the computation of Yukawa couplings. We introduce all necessary concepts and tools such as the basics of toric geometry, resolution of singularities, construction of mirror pairs, Picard-Fuchs equations, etc. and illustrate all of this on a non-trivial example. Extended version of a lecture given at the Third Baltic Student Seminar, Helsinki September 1993Comment: LMU-TPW-94-02, 45 pages, harvma

Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces

We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton-corrected Yukawa couplings, and the topological one-loop partition function to the case of complete intersections with higher-dimensional moduli spaces. We will develop a new method of obtaining the instanton-corrected Yukawa couplings through a close study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the K\"ahler moduli fields induced from the ambient space for all complete intersections in non singular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three-generation models that are found in this class. We also apply our method to solve the simplest model in which a topology change was observed and discuss examples of complete intersections in singular ambient spaces.Comment: 50 page

Potential Profiling of the Nanometer-Scale Charge Depletion Layer in n-ZnO/p-NiO Junction Using Photoemission Spectroscopy

We have performed a depth-profile analysis of an all-oxide p-n junction diode n-ZnO/p-NiO using photoemission spectroscopy combined with Ar-ion sputtering. Systematic core-level shifts were observed during the gradual removal of the ZnO overlayer, and were interpreted using a simple model based on charge conservation. Spatial profile of the potential around the interface was deduced, including the charge-depletion width of 2.3 nm extending on the ZnO side and the built-in potential of 0.54 eV

Mechanism of phase transitions and the electronic density of states in (La,Sm)FeAsO1−x_{1-x}Fx_x from ab initio calculations

The structure and electronic density of states in layered LnFeAsO$_{1-x}$F$_x$ (Ln=La,Sm; $x$=0.0, 0.125, 0.25) are investigated using density functional theory. For the $x$=0.0 system we predict a complex potential energy surface, formed by close-lying single-well and double-well potentials, which gives rise to the tetragonal-to-orthorhombic structural transition, appearance of the magnetic order, and an anomaly in the specific heat capacity observed experimentally at temperatures below $\sim$140--160 K. We propose a mechanism for these transitions and suggest that these phenomena are generic to all compounds containing FeAs layers. For $x>$0.0 we demonstrate that transition temperatures to the superconducting state and their dependence on $x$ correlate well with the calculated magnitude of the electronic density of states at the Fermi energy.Comment: 4 pages, 3 figures, 1 tabl

Exceptional String: Instanton Expansions and Seiberg-Witten Curve

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to obtain the Seiberg--Witten curve of E-string with arbitrary Wilson lines with the help of elliptic functions.Comment: 71 pages, three Wilson line

LaCo2B2: A Co-based layered superconductor with a ThCr2Si2-type structure

LaCo2B2 with a ThCr2Si2-type structure composed of alternately stacked La and CoB layers exhibits metallic electrical conductivity and Pauli paramagnetic behavior down to 2K. Bulk superconductivity with a Tc of ~4K emerges upon substitution with dopant elements; i.e., isovalent substitution to form (La1-xYx)Co2B2, or aliovalent substitution to form La(Co1-xFex)2B2. Highly covalent bonding between Co 3d and B 2p levels in the CoB layers, which is caused by the B 2p level being shallower than the Fermi level, removes magnetic ordering from Co 3d electrons even in the undoped samples.Comment: 3 figure

A Simple Algebraic Derivation of the Covariant Anomaly and Schwinger Term

An expression for the curvature of the "covariant" determinant line bundle is given in even dimensional space-time. The usefulness is guaranteed by its prediction of the covariant anomaly and Schwinger term. It allows a parallel derivation of the consistent anomaly and Schwinger term, and their covariant counterparts, which clarifies the similarities and differences between them. In particular, it becomes clear that in contrary to the case for anomalies, the difference between the consistent and covariant Schwinger term can not be extended to a local form on the space of gauge potentials.Comment: 16 page

Non-Supersymmetric Stringy Attractors

In this paper we examine the stability of non-supersymmetric attractors in type IIA supergravity compactified on a Calabi-Yau manifold, in the presence of sub-leading corrections to the N=$ pre-potential. We study black hole configurations carrying D0-D6 and D0-D4 charges. We consider the O(1) corrections to the pre-potential given by the Euler number of the Calabi-Yau manifold. We argue that such corrections in general can not lift the zero modes for the D0-D6 attractors. However, for the attractors carrying the D0-D4 charges, they affect the zero modes in the vector multiplet sector. We show that, in the presence of such O(1) corrections, the D0-D4 attractors can either be stable or unstable depending on the geometry of the underlying Calabi-Yau manifold, and on the specific values of the charges they carry.Comment: corrected typos, minor modification