Exact results for Wilson loops in orbifold ABJM theory

Hao Ouyang; Jun-Bao Wu; Jia-Ju Zhang

doi:10.1088/1674-1137/40/8/083101

Chinese Physics C> 2016, Vol. 40> Issue(8) : 083101 DOI: 10.1088/1674-1137/40/8/083101

Exact results for Wilson loops in orbifold ABJM theory

Hao Ouyang ^1,2,, ,
Jun-Bao Wu ^1,2,3,, ,
Jia-Ju Zhang ^1,2,,

1.
Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049, China
2.
Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049, China
3.
Center for High Energy Physics, Peking University, 5 Yiheyuan Rd, Beijing 100871, China

Abstract
HTML
Reference
Related

PDF

Abstract：
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d=3 N=4 super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition function of the N=4 orbifold ABJM theory has been computed previously in the literature. In this paper, we re-derive it using a slightly different method. We calculate the vacuum expectation values of the circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2 BPS Wilson loops in arbitrary representations. We use both the saddle point approach and Fermi gas approach. The results for Wilson loops are in accord with the available gravity results.
- AdS/CFT correspondence ,
- Wilson loop ,
- Chern-Simons theory ,
- matrix model

References

[1]	J. M. Maldacena, Int. J. Theor. Phys., 38: 1113-1133 (1999); Adv. Theor. Math. Phys. 2: 231 (1998)
[2]	S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B, 428: 105-114 (1998)
[3]	E. Witten, Adv. Theor. Math. Phys., 2: 253-291 (1998)
[4]	J. M. Maldacena, Phys. Rev. Lett., 80: 4859-4862 (1998)
[5]	S.-J. Rey and J.-T. Yee, Eur. Phys. J. C, 22: 379-394 (2001)
[6]	D. E. Berenstein, R. Corrado, W. Fischler et al, Phys. Rev. D, 59: 105023 (1999)
[7]	N. Drukker, D. J. Gross, and H. Ooguri, Phys. Rev. D, 60: 125006 (1999)
[8]	J. Erickson, G. Semenoff, and K. Zarembo, Nucl. Phys. B, 582: 155-175 (2000)
[9]	N. Drukker and D. J. Gross, J. Math. Phys., 42: 2896-2914 (2001)
[10]	V. Pestun, Commun. Math. Phys., 313: 71-129 (2012)
[11]	O. Aharony, O. Bergman, D. L. Jafferis et al, JHEP, 0810: 091 (2008)
[12]	N. Drukker, J. Plefka, and D. Young, JHEP, 0811: 019 (2008)
[13]	B. Chen and J.-B. Wu, Nucl. Phys. B, 825: 38-51 (2010)
[14]	S.-J. Rey, T. Suyama, and S. Yamaguchi, JHEP, 0903: 127 (2009)
[15]	N. Drukker and D. Trancanelli, JHEP, 1002: 058 (2010)
[16]	D. Gaiotto and X. Yin, JHEP, 0708: 056 (2007)
[17]	A. Kapustin, B. Willett, and I. Yaakov, JHEP, 1003: 089 (2010)
[18]	D. L. Jafferis, JHEP, 1205: 159 (2012)
[19]	N. Hama, K. Hosomichi, and S. Lee, JHEP, 1103: 127 (2011)
[20]	M. Marino and P. Putrov, JHEP, 1006: 011 (2010)
[21]	N. Drukker, M. Marino, and P. Putrov, Commun. Math. Phys., 306: 511-563 (2011)
[22]	C. P. Herzog, I. R. Klebanov, S. S. Pufu et al, Phys. Rev. D, 83: 046001 (2011)
[23]	M. Marino and P. Putrov, J. Stat. Mech., 1203: P03001 (2012)
[24]	A. Klemm, M. Marino, M. Schiereck et al, Z. Naturforsch. A, 68: 178-209 (2013)
[25]	Y. Hatsuda, M. Honda, S. Moriyama et al, JHEP, 1310: 168 (2013)
[26]	M. Benna, I. Klebanov, T. Klose et al, JHEP, 0809: 072 (2008)
[27]	Y. Imamura and K. Kimura, Prog. Theor. Phys., 120: 509-523 (2008)
[28]	S. Terashima and F. Yagi, JHEP, 0812: 041 (2008)
[29]	Y. Imamura and K. Kimura, JHEP, 0810: 040 (2008)
[30]	M. Honda and S. Moriyama, JHEP, 1408: 091 (2014)
[31]	H. Ouyang, J.-B. Wu, and J.-j. Zhang, JHEP, 1511: 213 (2015)
[32]	M. Cooke, N. Drukker, and D. Trancanelli, JHEP, 1510: 140 (2015)
[33]	Y. Hatsuda, S. Moriyama, and K. Okuyama, JHEP, 1301: 158 (2013)
[34]	M. Hanada, M. Honda, Y. Honma et al, JHEP, 05: 121 (2012)
[35]	Y. Hatsuda and K. Okuyama, JHEP, 1410: 158 (2014)
[36]	H. Fuji, S. Hirano, and S. Moriyama, JHEP, 1108: 001 (2011)
[37]	G. Olshanski, A. Regev, and A. Vershik, arXiv:math/0110077
[38]	M. Aganagic, R. Dijkgraaf, A. Klemm et al, Commun. Math. Phys., 261: 451-516 (2006)
[39]	H. Ouyang, J.-B. Wu, and J.-j. Zhang, Eur. Phys. J. C, 75: 606 (2015)
[40]	D. Gaiotto and E. Witten, JHEP, 1006: 097 (2010)
[41]	K. Hosomichi, K.-M. Lee, S. Lee et al, JHEP, 0807: 091 (2008)
[42]	F.-M. Chen and Y.-S. Wu, JHEP, 1302: 016 (2013)
[43]	F.-M. Chen and Y.-S. Wu, arXiv:1212.6650
[44]	D. L. Jafferis and A. Tomasiello, JHEP, 0810: 101 (2008)
[45]	S. Hohenegger and I. Kirsch, JHEP, 0904: 129 (2009)
[46]	D. Gaiotto and D. L. Jafferis, JHEP, 1211: 015 (2012)
[47]	Y. Hikida, W. Li, and T. Takayanagi, JHEP, 0907: 065 (2009)
[48]	S. Moriyama and T. Nosaka, JHEP, 1411: 164 (2014)
[49]	Y. Hatsuda, M. Honda, and K. Okuyama, JHEP, 09: 046 (2015)
[50]	M. S. Bianchi, G. Giribet, M. Leoni et al, Phys. Rev. D, 88: 026009 (2013)
[51]	M. S. Bianchi, G. Giribet, M. Leoni et al, JHEP, 1310: 085 (2013)
[52]	L. Griguolo, G. Martelloni, M. Poggi et al, JHEP, 1309: 157 (2013)
[53]	K.-M. Lee and S. Lee, JHEP, 1009: 004 (2010)

[1]	Xi-Hao Fang , Fang-Zhong Chen , Jia-Rui Sun . Surface growth approach for bulk reconstruction in the AdS/BCFT correspondence. Chinese Physics C, 2024, 48(6): 065106. doi: 10.1088/1674-1137/ad32be
[2]	Hong-Zhe Zhang , Wan-Zhe Feng , Jun-Bao Wu . Holographic operator product expansion of loop operators in the ${{ \mathcal N} {\bf{=4}}\sim {\boldsymbol {S O(N)}}} $ super Yang-Mills theory. Chinese Physics C, 2023, 47(8): 083101. doi: 10.1088/1674-1137/acd364
[3]	Yue Ding , Zi-qiang Zhang . Holographic Schwinger effect in a soft wall AdS/QCD model. Chinese Physics C, 2021, 45(1): 013111. doi: 10.1088/1674-1137/abc240
[4]	Jing-Bo Wang , Chao-Guang Huang . Conformal field theory on the horizon of a BTZ black hole. Chinese Physics C, 2018, 42(12): 123110. doi: 10.1088/1674-1137/42/12/123110
[5]	Taejin Lee . Covariant open string field theory on multiple Dp-branes. Chinese Physics C, 2018, 42(11): 113105. doi: 10.1088/1674-1137/42/11/113105
[6]	Yi-dian Chen , Mei Huang . Two-gluon and trigluon glueballs from dynamical holography QCD. Chinese Physics C, 2016, 40(12): 123101. doi: 10.1088/1674-1137/40/12/123101
[7]	HUO Qiu-Hong , JIANG Yun-Guo , WANG Ru-Zhi , YAN Hui . Anomalous spin of the Chern-Simons-Georgi-Glashow model. Chinese Physics C, 2013, 37(4): 043104. doi: 10.1088/1674-1137/37/4/043104
[8]	WANG Hong-Min , HOU Zhao-Yu , LIU Jia-Fu , SUN Xian-Jing . Charm structure functions and gluon shadowing effects with the AdS/CFT model. Chinese Physics C, 2012, 36(8): 691-696. doi: 10.1088/1674-1137/36/8/002
[9]	LU Zhun . Comparing AdS/CFT dipole model to HERA F₂ data. Chinese Physics C, 2010, 34(9): 1421-1424. doi: 10.1088/1674-1137/34/9/060
[10]	WANG Ke , JIANG Yun-Guo , HUO Qiu-Hong . Quantal symmetries in the non-linear σ model with Maxwell and non-Abelian Chern-Simons terms. Chinese Physics C, 2010, 34(5): 535-538. doi: 10.1088/1674-1137/34/5/003
[11]	WANG Yong-Long , LI Zi-Ping . Symmetries in the Non-linear Sigma Model with Maxwell-Chern-Simons Term. Chinese Physics C, 2004, 28(7): 696-698.
[12]	LONG Zheng-Wen , LIU Bo , LI Zi-Ping . Canonical Quantization of the Complex Scalar Field Coupled to the Abel Chern-Simons Term. Chinese Physics C, 2003, 27(10): 866-869.
[13]	LI Rui-Jie , LI Zi-Ping . Quantal Canonical Symmetries in Spinor QED with Chern-Simons Term. Chinese Physics C, 2002, 26(4): 325-330.
[14]	Jiang Jinhuan , Li Ziping . Quantization of a Scalar QED With Chern-Simons Term in the Batalin-Fradkin-Vilkovisky Scheme. Chinese Physics C, 1999, 23(8): 784-789.
[15]	Zhang Zhihe , Li Ziping . Casimir Effect of the Maxwell- Chern-Simons Field. Chinese Physics C, 1998, 22(1): 87-91.
[16]	Chen Min , Hou Boyu , Shi Kangjie . Reflection Matrix of Z_n Belavin Model. Chinese Physics C, 1996, 20(S4): 325-331.
[17]	Guo Shuohong , Fang Xiyan . Quantization of Lattice Chern-Simons Theory. Chinese Physics C, 1994, 18(8): 706-714.
[18]	CHEN Qi-Zhou , LI Zhi-Bing , LUO Xiang-Qian , DAI Fu-Hua , GUO Shuo-Hong . VACUUM EXPECTATION VALUES OF 6-LINK WILSON LOOP IN SU(2) LATTICE GAUGE THEORY. Chinese Physics C, 1990, 14(3): 212-219.
[19]	ZHOU Guang-Zhao , WU Yue-Liang , XIE Yan-Bo . THE GENERAL CHERN-SIMONS COCHAIN AND THEIR APPLICATION. Chinese Physics C, 1986, 10(2): 177-185.
[20]	XUE She-Sheng , XIAN Ding-Chang . THE STOCHASTIC EQUATIONS IN THE LATTICE GAUGE FIELD THEORY AND THE SCHWINGER-KYSON EQUATION FOR THE WILSON LOOP VARIABLE. Chinese Physics C, 1985, 9(6): 703-711.

Access

Get Citation

Hao Ouyang, Jun-Bao Wu and Jia-Ju Zhang. Exact results for Wilson loops in orbifold ABJM theory[J]. Chinese Physics C, 2016, 40(8): 083101. doi: 10.1088/1674-1137/40/8/083101

Hao Ouyang, Jun-Bao Wu and Jia-Ju Zhang. Exact results for Wilson loops in orbifold ABJM theory[J]. Chinese Physics C, 2016, 40(8): 083101. doi: 10.1088/1674-1137/40/8/083101 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2016-01-18
Revised: 2016-03-04

Fund

Supported by NSFC (11222549, 11575202), K. C. Wong Education Foundation and Youth Innovation Promotion Association of CAS (2011016)

Article Metric

Article Views(1662)
PDF Downloads(90)
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

Exact results for Wilson loops in orbifold ABJM theory

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Exact results for Wilson loops in orbifold ABJM theory

Corresponding author: Hao Ouyang,

Corresponding author: Jun-Bao Wu,

Corresponding author: Jia-Ju Zhang,

HTML

目录