9 research outputs found
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
Gravitational corrections in supersymmetric gauge theory and matrix models
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are
obtained from topological string amplitudes. We show how they are recovered in
matrix model computations. This provides a test of the proposal by Dijkgraaf
and Vafa beyond the planar limit. Both, matrix model and topological string
theory, are used to check a conjecture of Nekrasov concerning these
gravitational couplings in Seiberg-Witten theory. Our analysis is performed for
those gauge theories which are related to the cubic matrix model, i.e. pure
SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic
superpotential. We outline the computation of the topological amplitudes for
the local Calabi-Yau manifolds which are relevant for these two cases.Comment: 27 pages, one eps figur