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

Topological String Partition Functions as Polynomials

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus.Comment: 22 pages, 6 figures. v2:typos correcte

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

Experimental evidence of TcT_c enhancement without the influence of spin fluctuations: NMR study on LaFeAsO_{1-x}H_x under a pressure of 3.0 GPa

The electron-doped high-transition-temperature (T_c) iron-based pnictide superconductor LaFeAsO_{1-x}H_x has a unique phase diagram: superconducting (SC) double domes are sandwiched by antiferromagnetic phases at ambient pressure and they turn to a single dome with a maximum T_c that exceeds 45K at a pressure of 3.0 GPa. We studied whether spin fluctuations are involved in increasing T_c under a pressure of 3.0 GPa by using ^{75}As nuclear magnetic resonance (NMR) technique. The ^{75}As-NMR results for the powder samples show that T_c increases up to 48 K without the influence of spin fluctuations. The fact indicates that spin fluctuations are not involved in raising T_c, which implies that other factors, such as orbital degrees of freedom, may be important for achieving a high T_c of almost 50 K.Comment: Correponding Author: Naoki Fujiwar