Local mirror symmetry of curves: Yukawa couplings and genus 1

Brian Forbes, Masao Jinzenji

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We continue our study of equivariant local mirror symmetry of curves, i.e., mirror symmetry for Xk - O(k) ⊕ O(-2 - k) → ℙ1 with torus action (λ12) on the bundle. For the antidiagonal action λ1 = - λ2, we find closed formulas for the mirror map, a rational B model Yukawa coupling and consequently Picard-Fuchs equations for all k. Moreover, we give a simple closed form for the B model genus 1 Gromov-Witten potential. For the diagonal action λ1 = λ2, we argue that the mirror symmetry computation is equivalent to that of the projective bundle ℙ(O ⊕ O(k) ⊕O(-2 - k)) → ℙ1. Finally, we outline the computation of equivariant Gromov-Witten invariants for An singularities and toric tree examples via mirror symmetry.

Original languageEnglish
Pages (from-to)175-197
Number of pages23
JournalAdvances in Theoretical and Mathematical Physics
Volume11
Issue number1
DOIs
Publication statusPublished - 2007
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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