TY - JOUR

T1 - Quantum mirror curve of periodic chain geometry

AU - Kimura, Taro

AU - Sugimoto, Yuji

N1 - Funding Information:
We would like to thank Andrea Brini for helpful discussion. Y.S. was supported in part by the JSPS Research Fellowship for Young Scientists (No. JP17J00828). The work of TK was supported in part by Keio Gijuku Academic Development Funds, JSPS Grant-in-Aid for Scientific Research (No. JP17K18090), MEXT-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (No. S1511006), JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (No. JP15H05855), and “Discrete Geometric Analysis for Materials Design” (No. JP17H06462).
Publisher Copyright:
© 2019, The Author(s).

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 -