Mirror symmetry, D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds

ZHANG Shan-Shan; YANG Fu-Zhong

doi:10.1088/1674-1137/39/12/121002

Chinese Physics C> 2015, Vol. 39> Issue(12) : 121002 DOI: 10.1088/1674-1137/39/12/121002

Mirror symmetry, D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds

ZHANG Shan-Shan ,
YANG Fu-Zhong ^,

1.
School of Physical Sciences, University of Chinese Academy of Sciences, Yuquan Road 19 A, Beijing 100049, China

Abstract
HTML
Reference
Related

PDF

Abstract：
The D-brane superpotential is very important in the low energy effective theory. As the generating function of all disk instantons from the worldsheet point of view, it plays a crucial role in deriving some important properties of the compact Calabi-Yau manifolds. By using the generalized GKZ hypergeometric system, we will calculate the D-brane superpotentials of two non-Fermat type compact Calabi-Yau hypersurfaces in toric varieties, respectively. Then according to the mirror symmetry, we obtain the A-model superpotentials and the Ooguri-Vafa invariants for the mirror Calabi-Yau manifolds.
- D-brane ,
- superpotential ,
- mirror symmetry ,
- Ooguri-Vafa invariant

References

[1]	Hosono S, Klemm A, Theisen S et al. Nucl. Phys. B, 1995, 433: 501-554
[2]	Berglund P, Katz P, Klemm A. Nucl. Phys. B, 1995, 456: 153-204
[3]	Alim M, Hecht M, Mayr P et al. JHEP, 2011, 1106: 103
[4]	Lerche W, Vafa C, Warner N. Nucl. Phys. B, 1989, 324: 427
[5]	Jockers H, Soroush M. Commun. Math. Phys., 2009, 290: 249-290
[6]	Hosono S, lian B H, Yau S T et al. Commun. Math. Phys., 1996, 182: 535-578
[7]	Walcher J. Commun. Math. Phys., 2007, 276: 671-689
[8]	Morrison D R, Walcher J. arXiv: hepth/0709.4028
[9]	Grimm T W, Ha T W, Klemm A et al. Nucl. Phys. B, 2009, 816: 139-184
[10]	Candelas P, Font A, Katz S et al. Nucl. Phys. B, 1994, 429: 626-674
[11]	Douglas M R, Govindarajan S, Jayaraman T et al. Commun. Math. Phys., 2004, 248: 85-118
[12]	Aspinwall P S. arXiv: hepth/0403166
[13]	XU Feng-Jun, YANG Fu-Zhong. Chin. Phys. C, 2014, 38(3): 033103
[14]	CHENG Shi, XU Feng-Jun, YANG Fu-Zhong. Modern Physics Letters A, 2014, 29(12): 1450061
[15]	XU Feng-Jun, YANG Fu-Zhong. Modern Physics Letters A, 2014, 29(13): 1450062
[16]	XU Feng-Jun, YANG Fu-Zhong, Chin. Phys. C, 2015, 39(4): 043102
[17]	Fuji H, Nakayama S, Shimizu M et al. arXiv: hepth/1011.2347
[18]	Baumgartl M, Brunner L, Gaberdiel M R. JHEP, 2007, 0707: 061
[19]	Witten E. Prog. Math., 1995, 133: 637-678
[20]	Witten E. Nucl. Phys. B, 1997, 507: 658-690
[21]	Aganagic M, Vafa C. arXiv: hepth/0012041
[22]	YANG Fu-Zhong. Commun. Theor. Phys., 2003, 40: 537-542
[23]	Aganagic M, Klemm A, Vafa C. Z. Naturforsch. A, 2002, 57: 1-28
[24]	Witten E. Nucl. Phys. B, 1993, 403: 159-222
[25]	Mayr P. Adv. Theor. Math. Phys., 2002, 5: 213-242
[26]	Dauglas M R, Kachru S. Rev. Mod. Phys., 2007, 79: 733-796
[27]	Haack M, Louis J. Phys. Lett. B, 2001, 507: 296-304
[28]	Grimm T W, Ha T W, Klemm A et al. arXiv: hepth/0909.2025
[29]	Gukov S, Vafa C, Witten E. Nucl. Phys. B, 2000, 584: 69-108
[30]	Lerche W, Mayr P, Warner N. arXiv: hepth/0207259
[31]	Lerche W, Mayr P, Warner N. arXiv: hepth/0208039
[32]	Si-Li, Lian B H, Yau S T. arXiv: hepth/0910.4215
[33]	Clemens H. arXiv: hepth/0206219
[34]	Baumgartl M, Brunner L, Soroush M. Nucl. Phys. B, 2011, 843: 602-637
[35]	Alim M, Hecht M, Mayr P et al. arXiv:0901.2937
[36]	Ooguri H, Vafa C. Nucl. Phys. B, 2000, 577: 419-438
[37]	Walcher J. arXiv: hepth/0904.4905
[38]	Gel'fand I M, Zelevinski A, Kapranov M. Funct. Anal. Appl., 1989, 28: 94
[39]	Batyrev V V. arXiv: hepth/9310003
[40]	Batyrev V V, Straten D V. Commun. Math. Phys., 1995, 168: 493
[41]	Hosono S, Klemm A, Theisen S et al. Commun. Math. Phys., 1995, 167: 301-350
[42]	Hosono S. GKZ System. arXiv: hepth/9707003
[43]	Alim M, Hecht M, Jockers H et al. Nucl. Phys. B, 2010, 841: 303-338
[44]	Aganagic M, Beem C. JHEP, 2011, 1112: 060
[45]	Aganagic M, Klemm A, Marino M et al. Commun. Math. Phys., 2005, 254: 452-478
[46]	Candelas P, Ossa X, Katz S. Nucl. Phys. B, 1995, 450: 267-292
[47]	Grimm T W, Klemm, Klevers D. JHEP, 2011, 1105: 113

[1]	Xiao-Tian Jiang , Fu-Zhong Yang . Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F -theory duality. Chinese Physics C, 2018, 42(9): 093104. doi: 10.1088/1674-1137/42/9/093104
[2]	XU Feng-Jun , YANG Fu-Zhong . D-brane superpotentials and Ooguri-Vafa invariants of compact Calabi-Yau threefolds. Chinese Physics C, 2015, 39(4): 043102. doi: 10.1088/1674-1137/39/4/043102
[3]	XU Feng-Jun , YANG Fu-Zhong . Off-shell superpotentials and Ooguri-Vafa invariants of type Ⅱ/F theory compactification. Chinese Physics C, 2014, 38(3): 033103. doi: 10.1088/1674-1137/38/3/033103
[4]	LIU Bei-Bei , OUYANG Fei , CHEN Wei . Influence of coupling constants on nuclear symmetry energy. Chinese Physics C, 2013, 37(4): 044103. doi: 10.1088/1674-1137/37/4/044103
[5]	LIU Min , LI Zhu-Xia , WANG Ning , ZHANG Feng-Shou . Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei. Chinese Physics C, 2011, 35(7): 629-634. doi: 10.1088/1674-1137/35/7/006
[6]	LI Fang-Qiong , ZHAO Peng-Wei , LIANG Hao-Zhao . Perturbative pseudospin symmetry limit with linear spin-orbit potential. Chinese Physics C, 2011, 35(9): 825-828. doi: 10.1088/1674-1137/35/9/007
[7]	DONG Hong-Fei , BAI Hong-Bo , . Isospin and mixed symmetry structure in ²⁶Mg. Chinese Physics C, 2011, 35(9): 817-820. doi: 10.1088/1674-1137/35/9/005
[8]	LI Kang , Dulat Sayipjamal , . Non-commutative phase space and its space-time symmetry. Chinese Physics C, 2010, 34(7): 944-948. doi: 10.1088/1674-1137/34/7/003
[9]	L. Ya. Glozman . Chiral symmetry restoration in excited hadrons and dense matter. Chinese Physics C, 2010, 34(9): 1212-1217. doi: 10.1088/1674-1137/34/9/012
[10]	GUO Feng-Kun . Heavy quark spin symmetry and heavy flavor hadronic molecules. Chinese Physics C, 2010, 34(9): 1294-1297. doi: 10.1088/1674-1137/34/9/027
[11]	MAO Shi-Jun , HUANG Xu-Guang , ZHUANG Peng-Fei . Viscosities in chiral symmetry breaking phase. Chinese Physics C, 2010, 34(9): 1440-1442. doi: 10.1088/1674-1137/34/9/065
[12]	LI Jia-Xing , LIU Ping-Ping , WANG Jian-Song , HU Zheng-Guo , MAO Rui-Shi , SUN Zhi-Yu , LI Chen , CHEN Ruo-Fu , XU Hu-Shan , XIAO Guo-Qing , GUO Zhong-Yan . Measurement of the total reaction cross section for the mirror nuclei ¹²N and ¹²B. Chinese Physics C, 2010, 34(4): 452-455. doi: 10.1088/1674-1137/34/4/006
[13]	C. Garcia-Recio , V. K. Magas , T. Mizutani , J. Nieves , A. Ramos , L. L. Salcedo . Charmed baryon resonances with heavy-quark symmetry. Chinese Physics C, 2009, 33(12): 1323-1326. doi: 10.1088/1674-1137/33/12/046
[14]	MAO Cheng-Wen , XI Zai-Jun , YU Xiao-Han , XIAO Ti-Qiao . Design optimization of a tapered mirror for microfocusing optics. Chinese Physics C, 2009, 33(8): 687-690. doi: 10.1088/1674-1137/33/8/017
[15]	LÜ Li-Jun , BAI Hong-Bo , ZHANG Jin-Fu . Isospin and mixed symmetry structure in ²⁴Mg. Chinese Physics C, 2008, 32(3): 177-181. doi: 10.1088/1674-1137/32/3/003
[16]	ZHENG Yong-Nan , ZHOU Dong-Mei , YUAN Da-Qing , ZHANG Xi-Zhen , ZUO Yi , XU Yong-Jun , ZHU Jia-Zheng , WANG Zhi-Qiang , LUO Hai-Long , FAN Ping , ZHU Sheng-Yun . Magnetic moment measurements of mirror nuclei ¹²B and ¹²N. Chinese Physics C, 2008, 32(S2): 174-176.
[17]	JIA Bei , LI Xi-Guo , ZHANG Peng-Ming . Angular momentum of a brane-world model. Chinese Physics C, 2008, 32(11): 865-867. doi: 10.1088/1674-1137/32/11/003
[18]	Li Ziping . Canonical Symmetry in a System with Singular Lagrangian and Ward Identities. Chinese Physics C, 1994, 18(S3): 265-274.
[19]	Zhao Liu , Yang Wenli . Bosonic Superconformal Toda Theory and Dressing Symmetry. Chinese Physics C, 1993, 17(S1): 65-72.
[20]	Liu Baohua , Li Jiarong . The Mean-Field Analysis for Chiral Symmetry Phase Transition. Chinese Physics C, 1988, 12(S4): 373-378.

Access

Get Citation

ZHANG Shan-Shan and YANG Fu-Zhong. Mirror symmetry, D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds[J]. Chinese Physics C, 2015, 39(12): 121002. doi: 10.1088/1674-1137/39/12/121002

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2015-03-09
Revised: 2015-07-14

Fund

Supported by Y4JT01VJ01 and NSFC(11475178)

Article Metric

Article Views(1664)
PDF Downloads(46)
Cited by(0)

Policy on re-use

To reuse of Open Access content published by CPC, for content published under the terms of the Creative Commons Attribution 3.0 license (“CC CY”), the users don’t need to request permission to copy, distribute and display the final published version of the article and to create derivative works, subject to appropriate attribution.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Mirror symmetry, D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds

Corresponding author: YANG Fu-Zhong,

1. School of Physical Sciences, University of Chinese Academy of Sciences, Yuquan Road 19 A, Beijing 100049, China

Received Date: 2015-03-09

Accepted Date: 2015-07-14

Available Online: 2015-12-20

Fund Project: Supported by Y4JT01VJ01 and NSFC(11475178)

Abstract: The D-brane superpotential is very important in the low energy effective theory. As the generating function of all disk instantons from the worldsheet point of view, it plays a crucial role in deriving some important properties of the compact Calabi-Yau manifolds. By using the generalized GKZ hypergeometric system, we will calculate the D-brane superpotentials of two non-Fermat type compact Calabi-Yau hypersurfaces in toric varieties, respectively. Then according to the mirror symmetry, we obtain the A-model superpotentials and the Ooguri-Vafa invariants for the mirror Calabi-Yau manifolds.

HTML

Reference (47)

Mirror symmetry, D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article