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

Detection of antiferromagnetic ordering in heavily doped LaFeAsO1-xHx pnictide superconductors using nuclear-magnetic-resonance techniques

We studied double superconducting (SC) domes in LaFeAsO1-xHx by using 75As- and 1H-nuclear magnetic resonance techniques, and unexpectedly discovered that a new antiferromagnetic (AF) phase follows the double SC domes on further H doping, forming a symmetric alignment of AF and SC phases in the electronic phase diagram. We demonstrated that the new AF ordering originates from the nesting between electron pockets, unlike the nesting between electron and hole pockets as seen in the majority of undoped pnictides. The new AF ordering is derived from the features common to high-Tc pnictides: however, it has not been reported so far for other high-Tc pnictides because of their poor electron doping capability.Comment: 5 figures, in press in PR