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
SN - 1126-6708
VL - 2019
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 4
M1 - 147
ER -