### Abstract

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 language | English |
---|---|

Article number | 147 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2019 Apr 1 |

### Fingerprint

### Keywords

- String Duality
- Supersymmetric Gauge Theory
- Topological Strings

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2019*(4), [147]. https://doi.org/10.1007/JHEP04(2019)147

**Quantum mirror curve of periodic chain geometry.** / Kimura, Taro; Sugimoto, Yuji.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2019, no. 4, 147. https://doi.org/10.1007/JHEP04(2019)147

}

TY - JOUR

T1 - Quantum mirror curve of periodic chain geometry

AU - Kimura, Taro

AU - Sugimoto, Yuji

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

KW - String Duality

KW - Supersymmetric Gauge Theory

KW - Topological Strings

UR - http://www.scopus.com/inward/record.url?scp=85064950555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064950555&partnerID=8YFLogxK

U2 - 10.1007/JHEP04(2019)147

DO - 10.1007/JHEP04(2019)147

M3 - Article

AN - SCOPUS:85064950555

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 4

M1 - 147

ER -