String and Vortex

We discuss how the geometry of $D2$-$D0$ branes may be related to Gromov-Witten theory of Calabi-Yau threefolds.Comment: 31 page

Duality of Orbifoldized Elliptic Genera

We discuss duality and mirror symmetry phenomena of Landau-Ginzburg orbifolds considering their elliptic genera. Under the duality (or mirror) transform performed by orbifoldizing the Landau-Ginzburg model via some discrete group of the superpotential we observe that the roles of the untwisted and twisted sectors are exchanged. As explicit evidence detailed orbifold data are presented for $N=2$ minimal models, Arnold's exceptional singularities, $K3$ surfaces constructed from Arnold's singularities and Fermat hypersurfaces. (To appear in the proceedings of the workshop, ``Quantum Field Theory, Integrable Models and Beyond'', Yukawa Institute for Theoretical Physics, Kyoto University, 14-18 February 1994.)Comment: 27(portrait)+3(landscape) pages, LaTeX, KEK-TH-409. (one reference added

Higher-Rank Supersymmetry and Topological Field Theory

The $N=2$ minimal superconformal model can be twisted yielding an example of topological conformal field theory. In this article we investigate a Lie theoretic extension of this process.Comment: 10 page

Twisted Elliptic Genera of N=2 SCFTs in Two Dimensions

The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and the associated twisted Witten indices are investigated with due attention to their behaviors in orbifoldization. Our findings are illustrated by and applied to several concrete examples. We give a better understanding of the duality phenomenon observed long before for certain Landau-Ginzburg models. We revisit and prove an old conjecture of Witten which states that every ADE Landau-Ginzburg model and the corresponding minimal model share the same elliptic genus. Mathematically, we establish ADE generalizations of the quintuple product identity.Comment: 28 pages; v2 refs adde

Elliptic Genera of N=2 Hermitian Symmetric Space Models

Expressions are given for the elliptic genera of the Kazama-Suzuki models associated with hermitian symmetric spaces when the problems of field identifications are absent. We use the models' known Coulomb gas descriptions.Comment: 10 pages, LaTeX, KEK-TH-40