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A. Klemm

Publications and source records attributed to A. Klemm.

25 records · Page 2Linked to original sources
arXiv1994

Simple Singularities and N=2 Supersymmetric Yang-Mills Theory

We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to underly the quantum moduli space of $SU(n)$ N=2 supersymmetric gauge theory. These curves have an obvious generalization to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities. To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced. We also give some remarks on a possible relation to string theory.

hep-th↗
arXiv1994

A Note on ODEs from Mirror Symmetry

We give close formulas for the counting functions of rational curves on complete intersection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the instanton corrected Yukawa coupling.

hep-th↗
arXiv1994

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 Kähler 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.

hep-th↗
arXiv1994

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 1993

hep-th↗
arXiv1993

Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.

hep-th↗
arXiv1992

Landau-Ginzburg String Vacua

We investigate a class of (2,2) supersymmetric string vacua which may be represented as Landau--Ginzburg theories with a quasihomogeneous potential which has an isolated singularity at the origin. There are at least three thousand distinct models in this class. All vacua of this type lead to Euler numbers which lie in the range $-960 \leq χ\leq 960$. The Euler characteristics do not pair up completely hence the space of Landau--Ginzburg ground states is not mirror symmetric even though it exhibits a high degree of symmetry. We discuss in some detail the relation between Landau--Ginzburg models and Calabi--Yau manifolds and describe a subtlety regarding Landau--Ginzburg potentials with an arbitrary number of fields. We also show that the use of topological identities makes it possible to relate Landau-Ginzburg theories to types of Calabi-Yau manifolds for which the usual Landau-Ginzburg framework does not apply.

hep-th↗