Local mirror symmetry of curves: Yukawa couplings and genus 1

Abstract

We continue our study of equivariant local mirror symmetry of curves, i.e. mirror symmetry for X_k=O(k)+O(-2-k) over P^1 with torus action (lambda_1,lambda_2) on the bundle. For the antidiagonal action lambda_1=-lambda_2, we find closed formulas for the mirror map and a rational B model Yukawa coupling for all k. Moreover, we give a simple closed form for the B model genus 1 Gromov-Witten potential. For the diagonal action lambda_1=lambda_2, we argue that the mirror symmetry computation is equivalent to that of the projective bundle P(O+O(k)+O(-2-k)) over P^1. Finally, we outline the computation of equivariant Gromov-Witten invariants for A_n singularities and toric tree examples via mirror symmetry.

20 pages, no figures; v2: added details on connection to hep-th/0606120; v3: corrected triple intersection number, which gives sleek formula for Yukawa couplings

References in corpus (2)

• Phase transitions, double-scaling limit, and topological strings
• J functions, non-nef toric varieties and equivariant local mirror symmetry of curves

Cited by in corpus (7)

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• The local Gromov-Witten theory of CP^1 and integrable hierarchies
• Local B-model Yukawa couplings from A-twisted correlators
• Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points
• Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle
• On equivariant mirror symmetry for local P^2