Stefan Theisen

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 W(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.

Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

We discuss the emergence of

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

\mathcal{W} \mbox{-algebras}

On the vacuum structure of type II string compactifications on Calabi–Yau spaces with H-fluxes

as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) × SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical

Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces

{\mathcal{W}_3}\mbox{-algebra}

Nonperturbative effective actions of (N=2)-Supersymmetric gauge theories

with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant.

Gravitational corrections in supersymmetric gauge theory and matrix models

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.

Diffeomorphisms and Holographic Anomalies

We discuss the vacuum structure of type IIA/B Calabi-Yau string compactications to four dimensions in the presence of n-form H-fluxes. These will lift the vacuum degeneracy in the Calabi-Yau moduli space, and for generic points in the moduli space, N =2 supersymmetry will be broken. However, for certain ‘aligned’ choices of the H-flux vector, supersymmetric ground states are possible at the degeneration points of the CalabiYau geometry. We will investigate in detail the H-flux induced superpotential and the corresponding scalar potential at several degeneration points, such as the Calabi-Yau large volume limit, the conifold loci, the Seiberg-Witten points, the strong coupling point and the conformal points. Some emphasis is given to the question whether partial supersymmetry breaking can be realized at those points. We also relate the H-flux induced superpotential to the formalism of gauged N = 2 supergravity. Finally we point out the analogies between the Calabi-Yau vacuum structure due to H-fluxes and the attractor formalism of N = 2 black holes.

Modular invariance in supersymmetric field theories

Abstract 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 study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the Kahler moduli fields induced from the ambient space for all complete intersections in nonsingular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three-generation models which 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.

String Loop Corrections to the Universal Hypermultiplet

We elaborate on our previous work on N=2 supersymmetric Yang-Mills theory. In particular, we show how to explicitly determine the low energy quantum effective action for