Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F -theory duality

Xiao-Tian Jiang; Fu-Zhong Yang

doi:10.1088/1674-1137/42/9/093104

Chinese Physics C> 2018, Vol. 42> Issue(9) : 093104 DOI: 10.1088/1674-1137/42/9/093104

Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F -theory duality

Xiao-Tian Jiang ,
Fu-Zhong Yang ^,

1.
University of Chinese Academy of Sciences, Beijing 100049, China

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Abstract：
In this paper we study the parallel phase and the coincident phase of D-brane systems with the compactification of one closed modulus. D-brane systems with two phases are described by different 4-folds in terms of Type-Ⅱ/F-theory duality, and the phase transitions are related by the blow-up from a 4-fold with singularities to a 4-fold without. In terms of gauge theory, the phase transition corresponds to the enhancement of gauge group U(1)×U(1)→ U(2) connecting the Coulomb branch and the Higgs branch. For the sextic and octic with two D-branes, using mirror symmetry and Type-Ⅱ/F theory duality, A-model superpotentials are obtained from the B-model side for the two phases, and the U(1) Ooguri-Vafa invariants for the parallel phase and U(2) Ooguri-Vafa invariants for the coincident phase are extracted from the A-model superpotential. The difference between the invariants of the two phases is evidence of the phase transition between the Coulomb branch and the Higgs branch.
- Ooguri-Vafa invariants ,
- TypeⅡ/F-theory duality ,
- phase transition

References

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Xiao-Tian Jiang and Fu-Zhong Yang. Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F -theory duality[J]. Chinese Physics C, 2018, 42(9): 093104. doi: 10.1088/1674-1137/42/9/093104

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Received: 2018-04-02

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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

Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F -theory duality

Corresponding author: Fu-Zhong Yang,

1. University of Chinese Academy of Sciences, Beijing 100049, China

Received Date: 2018-04-02

Available Online: 2018-09-05

Fund Project: Supported by NSFC (11475178) and Y4JT01VJ01

Abstract: In this paper we study the parallel phase and the coincident phase of D-brane systems with the compactification of one closed modulus. D-brane systems with two phases are described by different 4-folds in terms of Type-Ⅱ/F-theory duality, and the phase transitions are related by the blow-up from a 4-fold with singularities to a 4-fold without. In terms of gauge theory, the phase transition corresponds to the enhancement of gauge group U(1)×U(1)→ U(2) connecting the Coulomb branch and the Higgs branch. For the sextic and octic with two D-branes, using mirror symmetry and Type-Ⅱ/F theory duality, A-model superpotentials are obtained from the B-model side for the two phases, and the U(1) Ooguri-Vafa invariants for the parallel phase and U(2) Ooguri-Vafa invariants for the coincident phase are extracted from the A-model superpotential. The difference between the invariants of the two phases is evidence of the phase transition between the Coulomb branch and the Higgs branch.

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Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F -theory duality

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