Quantum mirror curve of periodic chain geometry

Taro Kimura, Yuji Sugimoto

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The mirror curves enable us to study B-model topological strings on noncompact toric Calabi-Yau threefolds. One of the method to obtain the mirror curves is to calculate the partition function of the topological string with a single brane. In this paper, we discuss two types of geometries: one is the chain of N ℙ 1 ’s which we call “N-chain geometry,” the other is the chain of N ℙ 1 ’s with a compactification which we call “periodic N-chain geometry.” We calculate the partition functions of the open topological strings on these geometries, and obtain the mirror curves and their quantization, which is characterized by (elliptic) hypergeometric difference operator. We also find a relation between the periodic chain and ∞-chain geometries, which implies a possible connection between 5d and 6d gauge theories in the larte N limit.

Original languageEnglish
Article number147
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - 2019 Apr 1


  • String Duality
  • Supersymmetric Gauge Theory
  • Topological Strings

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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