Math @ Duke

Publications [#248091] of M. Ronen Plesser
Papers Published
 Morrison, DR; Plesser, MR, Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties,
Nuclear Physics B, vol. 440 no. 12
(April, 1995),
pp. 279354, Elsevier BV, ISSN 05503213 [9412236], [doi]
(last updated on 2019/02/16)
Abstract: 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 CalabiYau 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 "monomialdivisor mirror map" of Aspinwall, Greene and Morrison. © 1995.


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