Several aspects of (0,2) Landau-Ginzburg orbifolds are investigated. Especially the elliptic genera are computed in general and, for a class of models recently invented by Distler and Kachru, they are compared with the ones from (0,2) sigma models. Our formalism gives an easy way to calculate the generation numbers for lots of Distler-Kachru models even if they are based on singular Calabi-Yau spaces. We also make some general remarks on the BornOppenheimer calculation of the ground states elucidating its mathematical meaning in the untwisted sector. For Distler-Kachru models based on non-singular Calabi-Yau spaces we show that there exist 'residue' type formulas of the elliptic genera as well.hep-th/9402148 * JSPS fellow

We investigate D=4, N=1 F theory models realized by type IIB string compactification on toric threefolds. Massless spectra, gauge symmetries, phase transitions associated with divisor contractions and flops, and non-perturbative superpotentials are analyzed using elementary toric methods.

We investigate a (0,2) gauge theory realized on the world volume of the type IIB D1-brane at the singular point of a Calabi-Yau fourfold. It is argued that the gauge anomaly can be canceled via coupling to the R-R chiral bosons in bulk IIB string. We find that for a generic choice of the Fayet-Iliopoulos parameters on the world volume, the Higgs moduli space is a smooth fourfold birational to the original Calabi-Yau fourfold, but is not necessarily a Calabi-Yau manifold.

We investigate instanton expansions of partition functions of several toric Estring models using local mirror symmetry and elliptic modular forms. We also develop a method to determine the Seiberg-Witten curve of E-string with the help of elliptic functions.

No abstract