Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-12-30
Nucl.Phys.B440:279-354,1995
Physics
High Energy Physics
High Energy Physics - Theory
91 pages and 3 figures, harvmac with epsf (Changes in this version: one minor correction, one clarification, one new reference
Scientific paper
10.1016/0550-3213(95)00061-V
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 $M \subset V$. 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.
Morrison David R.
Plesser Ronen M.
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