紧致Calabi-Yau流形中D膜系统的超势和几何不变量

doi:10.7523/j.issn.2095-6134.2021.01.006

中国科学院大学学报 ›› 2021, Vol. 38 ›› Issue (1): 41-48.DOI: 10.7523/j.issn.2095-6134.2021.01.006

紧致Calabi-Yau流形中D膜系统的超势和几何不变量

李菲, 杨富中

中国科学院大学物理科学学院, 北京 100049

收稿日期:2019-04-02 修回日期:2019-04-26 发布日期:2021-03-05
通讯作者: 杨富中
基金资助:
Supported by the National Natural Science Foundation of China (11475178,Y4JT01VJ01)

The superpotential and geometric invariants of D-brane system on compact Calabi-Yau manifold

LI Fei, YANG Fuzhong

School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2019-04-02 Revised:2019-04-26 Published:2021-03-05
Supported by:
Supported by the National Natural Science Foundation of China (11475178,Y4JT01VJ01)

摘要/Abstract

摘要： 有效的D膜超势决定真空结构，是Ooguri-Vafa不变量的生成函数。它对物理和数学都具有重要意义。利用镜像对称性、GKZ系统和Type Ⅱ/F-理论对偶的方法，计算带有3个D膜的系统的超势；研究在紧致Calabi-Yau流形中，处于3个相中的D膜系统的超势和几何不变量。计算结果显示，这3个相区中得到的超势是不同的，这意味着增加的规范对称性和几何奇异性导致了相变。

关键词: 超弦理论, F-理论, 超势, Ooguri-Vafa不变量

Abstract: The effective D-brane superpotential determines the vacuum structure and is the generating function of the Ooguri-Vafa invariants. It is of great significance in both physics and mathematics. In this work, the superpotential of the system with three D-branes is calculated by mirror symmetry, GKZ-system (hypergeometric system of Gel’fand, Kapranov, and Zelevinski) method, and the type Ⅱ/F-theory duality. On compact Calabi-Yau manifold, the superpotenial and geometric invariants of D-brane system in the three phases are studied. The calculations show that the superpotentials in the three phases are different. This implies that the enhanced gauge symmetry in low energy theory and geometric singularity may lead to the phase transition.

Key words: superstring, F-theory, superpotential, Ooguri-Vafa invariants

中图分类号:

李菲, 杨富中. 紧致Calabi-Yau流形中D膜系统的超势和几何不变量[J]. 中国科学院大学学报, 2021, 38(1): 41-48.

LI Fei, YANG Fuzhong. The superpotential and geometric invariants of D-brane system on compact Calabi-Yau manifold[J]. Journal of University of Chinese Academy of Sciences, 2021, 38(1): 41-48.

参考文献

[1] Lerche W, Vafa C, Warner N P. Chiral rings in N=2 superconformal theories[J]. Nuclear Physics B, 1989, 324(2):427-474.
[2] Hosomo S, Klemm A, Theisen S, et al. Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces[J]. Communications in Mathematical Physics, 1995, 167(2):301-350.
[3] Lerche W, Mayr P, Warner N. N=1 special geometry, mixed Hodge variations and toric geometry[EB/OL]. arXiv:hep-th/0208039. (2002-08-06)[2019-03-01]. https//arxiv.org/abs/hep-th/0208039.
[4] Xu F J, Yang F Z. Off-shell superpotenials and Oogrui-Vafa invariants of type Ⅱ/F-theory compactfication[J]. Chinese Physics C, 2014, 38(3):033103.
[5] Xu F J, Yang F Z. Type Ⅱ/F-theory superpotentials and Ooguri-Vafa invariants of compact Calabi-Yau threefolds with three deformations[J]. Modern Physics Letters A, 2014, 29(13):1450062.
[6] Cheng S, Xu F J, Yang F Z. Off-shell D-brane/F-theory effective superpotentials and Ooguri-Vafa invariants of several compact Calabi-Yau manifolds[J]. Modern Physics Letters A, 2014, 29(12):1450061.
[7] Zhang S S, Yang F Z. Mirror Symmetry, D-brane superpotential and Ooguri-Vafa invariants of compact Calabi-Yau Manifolds[J]. Chinese Physics C, 2015, 39(12):121002.
[8] Zou H, Yang F Z. Effective superpotentials of type Ⅱ D-brane/F-theory on compact complete intersection CalabiYau Threefolds[J]. Modern Physics Letters A, 2016, 31(15):1650094.
[9] Jockers H, Soroush H. Effective superpotentials for compact D5-brane Calabi-Yau geometries[J]. Communications in Mathematical Physics, 2009, 290(1):249-290.
[10] Jockers H, Soroush M. Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurface[J]. Nuclear Physics B, 2009, 821(3):535-552.
[11] Alim M, Hecht M, Jockers H, et al. Hints for Off-Shell mirror symmetry in type Ⅱ/F-theory compactification[J]. Nuclear Physics B, 2010, 941(3):303-338.
[12] Berglund P, Mayr P. Non-perturbative superpotentials in F-theory and string duality[J]. Journal of High Energy Physics, 2013. Doi:10.1007/JHEP01(2013)114.
[13] Alim M, Hecht M, Mayr P, et al. Mirror symmetry for toric branes on compact hypersurfaces[J]. Journal of High Energy Physics, 2009. Doi:10.1088/1126-6708/2009/09/126.
[14] Hosono S, Lian B H, Yau S T. GKZ-generalized hypergeometric systems in mirror symmetry of Calabi-Yau hypersurfaces[J]. Communications in Mathematical Physics, 1996, 182(3):535-577.
[15] Jiang X T, Yang F Z. D-brane superpotentials, SU(2) Ooguri-Vafa invariants and type Ⅱ/F-theory duality[EB/OL]. arXiv:hep-th/1710.06184. (2018-04-06)[2019-03-01]. https://arxiv.org/abs/hep-th/1710.06184.
[16] Li S, Lian B H, Yau S T. Picard-Fuchs equations for relative periods and Abel-Jacobi map for Calabi-Yau hypersurfaces[J]. American Journal of Mathematics, 2012, 134(5):1345-1384.

紧致Calabi-Yau流形中D膜系统的超势和几何不变量

The superpotential and geometric invariants of D-brane system on compact Calabi-Yau manifold

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价

访问统计

联系我们