Certain perturbative aspects of two-dimensional sigma models with (0, 2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of “chiral differential operators” is related to sigma models. In the process, we obtain, for example, an understanding of the one-loop beta function in terms of holomorphic data. A companion paper will study nonperturbative behavior of these theories.

We formulate and prove a B-model disc level large $N$ duality result for general conifold transitions between compact Calabi-Yau spaces using degenerations of Hodge structures.

Felix FinsterA systematic procedure is developed for constructing fermion systems in discrete space–time which have a given outer symmetry. The construction is illustrated by simple examples. For the symmetric group, we derive constraints for the number of particles. In the physically interesting case of many particles and even more space–time points, this result shows that the permutation symmetry of discrete space–time is always spontaneously broken by the fermionic projector.

We consider Laplace transforms of the Picard–Fuchs differential equations of Calabi-Yau hypersurfaces and calculate their Stokes matrices. We also introduce two different types of Laplace transforms of Gelľfand-Kapranov-Zelevinski hypergeometric systems.