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

[1]	W. Lerche, P. Mayr, and N. Warner, arXiv:hep-th/0207259
[2]	W. Lerche, P. Mayr, and N. Warner, arXiv:hep-th/0208039
[3]	Mayr P, Adv. Theor. Math. Phys., 5:213-242 (2002)
[4]	M. Alim, M. Hecht, H. Jockers et al, arXiv:0909.1842
[5]	S. Gukov, C. Vafa, and E. Witten, Nucl. Phys. B, 584:69 (2000)
[6]	H. Jockers, P. Mayr, and J. Walcher, Adv. Theor. Math. Phys., 14.5:1433 (2010)
[7]	H. Jockers and M. Soroush, Commun. Math. Phys., 290:249 (2009)
[8]	Feng-Jun Xu and Fu-Zhong Yang, Chin. Phys. C, 38(3):33103-033103 (2014)
[9]	Feng-Jun Xu and Fu-Zhong Yang, Mod. Phys. Lett. A, 29.13:1450062 (2014)
[10]	Shi Cheng, Feng-Jun Xu, and Fu-Zhong Yang, Mod. Phys. Lett. A, 29.12:1450061 (2014)
[11]	Shan-Shan Zhang and Fu-Zhong Yang, Chin. Phys. C, 39(12):121002-121002 (2015)
[12]	Hao Zou and Fu-Zhong Yang, Mod. Phys. Lett. A, 31.15:1650094 (2016)
[13]	M. Alim, M. Hecht, P. Mayr, and A. Mertens, JHEP, 09:126 (2009)
[14]	V. V. Batyrev, J. Alg. Geom., 3:493 (1994)
[15]	S. Hosomo, A. Klemm, S. Theisen et al, Nucl. Phys. B, 433:501 (1995)
[16]	S. Hosono, B. H. Lian, and S.-T. Yau, Commun. Math. Phys., 182:535 (1996)
[17]	W. Fulton, Introduction to Toric Varieties, Princeton University Press, (Princeton, 1993)
[18]	M. Bershadsky and C. Vafa, Nucl. Phys. B, 463:398 (1996)
[19]	O. Fujino and H. Sato, arXiv:math/0307180v2
[20]	O. Fujino, arXiv:math/0112090v1
[21]	A. Scaramuzza, Smooth complete toric varieties:an algorithmic approach, Ph.D. Thesis, (University of Roma Tre, 2007)
[22]	C. V. Renesse, Combinatiorial aspects of toric varieties, Ph.D. Thesis, (University of Massachusetts Amherst, 2007)
[23]	E. Witten, Nucl. Phys. B, 403:159 (1993)

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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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Supported by NSFC (11475178) and Y4JT01VJ01

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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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