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

Abstract
HTML
Reference
Related

PDF

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)

[1]	Yu-Shan Wang , Zhen-Ming Xu , Bin Wu . Thermodynamic phase transition and winding number for the third-order Lovelock black hole. Chinese Physics C, 2024, 48(9): 095101. doi: 10.1088/1674-1137/ad53ba
[2]	Xu Ye , Zi-Qing Chen , Ming-Da Li , Shao-Wen Wei . QED effects on phase transition and Ruppeiner geometry of Euler-Heisenberg-AdS black holes. Chinese Physics C, 2022, 46(11): 115102. doi: 10.1088/1674-1137/ac814d
[3]	Haipeng An , Kun-Feng Lyu , Lian-Tao Wang , Siyi Zhou . A unique gravitational wave signal from phase transition during inflation. Chinese Physics C, 2022, 46(10): 101001. doi: 10.1088/1674-1137/ac76a7
[4]	Yun-Zhi Du , Huai-Fan Li , Fang Liu , Ren Zhao , Li-Chun Zhang . Phase transition of non-linear charged Anti-de Sitter black holes. Chinese Physics C, 2021, 45(11): 112001. doi: 10.1088/1674-1137/ac2049
[5]	Zhibin Li , Yidian Chen , Danning Li , Mei Huang . Locating the QCD critical end point through peaked baryon number susceptibilities along the freeze-out line. Chinese Physics C, 2018, 42(1): 053001. doi: 10.1088/1674-1137/42/1/013103
[6]	E. V. Mardyban , T. M. Shneidman , E. A. Kolganova , R. V. Jolos , S. -G. Zhou . Analytical description of shape transition in nuclearalternating parity bands. Chinese Physics C, 2018, 42(12): 124104. doi: 10.1088/1674-1137/42/12/124104
[7]	ZHOU Hou-Bing , DONG Guo-Xiang , SUN Xiao-Jun , XU Fu-Rong . Phase transition in odd-N Pd-isotopes. Chinese Physics C, 2015, 39(11): 114103. doi: 10.1088/1674-1137/39/11/114103
[8]	WANG Rui , CHEN Ying , GONG Ming , LIU Chuan , LIU Yu-Bin , LIU Zhao-Feng , MA Jian-Ping , MENG Xiang-Fei , ZHANG Jian-Bo . Phase transition in finite density and temperature lattice QCD. Chinese Physics C, 2015, 39(6): 063103. doi: 10.1088/1674-1137/39/6/063103
[9]	ZHANG Shan-Shan , YANG Fu-Zhong . Mirror symmetry, D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds. Chinese Physics C, 2015, 39(12): 121002. doi: 10.1088/1674-1137/39/12/121002
[10]	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
[11]	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
[12]	XU Xiao-Mei , FU Yong-Ping , LI Yun-De . η string formation in QCD chiral phase transition. Chinese Physics C, 2010, 34(4): 444-447. doi: 10.1088/1674-1137/34/4/004
[13]	LI Ang , PENG Guang-Xiong , Lombardo U . Deconfinement phase transition in neutron star matter. Chinese Physics C, 2009, 33(S1): 61-63. doi: 10.1088/1674-1137/33/S1/020
[14]	LIU Ying-Xin , QIN Shan , WU Jing , LI Xiao-Dong , LI Yan-Chun , LIU Jing . Pressure-induced phase transition of wulfenite. Chinese Physics C, 2009, 33(11): 1023-1027. doi: 10.1088/1674-1137/33/11/019
[15]	YANG Fang , SHEN Hong . Hadron-quark phase transition in neutron stars. Chinese Physics C, 2008, 32(S2): 77-80.
[16]	Zhang Fengshou , Ge Lingxiao . Static Theory for Nuclear Multifragmentation I. Phase Transition and Multifragmentation. Chinese Physics C, 1997, 21(S2): 63-72.
[17]	Li Panlin , Wu Hua , Xu Mengjie . Dynamics of Phase Transition Including Quark-Fragment Effects for an Expansion Quark-Gluon Plasma. Chinese Physics C, 1997, 21(S4): 55-64.
[18]	Hou Defu , Li Jiarong . Self-Consistent Investigation of Electroweak Transition at High Temperature. Chinese Physics C, 1994, 18(S4): 367-374.
[19]	Liu Baohua , Li Jiarong . The Mean-Field Analysis for Chiral Symmetry Phase Transition. Chinese Physics C, 1988, 12(S4): 373-378.
[20]	Wu Chongshi , Zeng Jinyan . Nuclear Pairing Phase Transition. Chinese Physics C, 1988, 12(S1): 81-90.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2018-04-02

Fund

Supported by NSFC (11475178) and Y4JT01VJ01

Article Metric

Article Views(1855)
PDF Downloads(21)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

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.

HTML

Reference (23)

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

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article