We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety V or a Calabi-Yau hypersurface M ⊂ V. In the linear model the instanton moduli spaces are relatively simple objects and the correlators are explicitly computable; moreover, the instantons can be summed, leading to explicit solutions for both kinds of models. In the case of smooth V, our results reproduce and clarify an algebraic solution of the V model due to Batyrev. In addition, we find an algebraic relation determining the solution for M in terms of that for V. Finally, we propose a modification of the linear model which computes instanton expansions about any limiting point in the moduli space. In the smooth case this leads to a (second) algebraic solution of the M model. We use this description to prove some conjectures about mirror symmetry, including the previously conjectured "monomial-divisor mirror map" of Aspinwall, Greene and Morrison.
Nuclear Physics B
- Pub Date:
- February 1995
- High Energy Physics - Theory;
- Mathematics - Algebraic Geometry
- 91 pages and 3 figures, harvmac with epsf (Changes in this version: one minor correction, one clarification, one new reference)