Note on non-vacuum conformal family contributions to R&eacute;nyi entropy in two-dimensional CFT

Jia-ju Zhang

doi:10.1088/1674-1137/41/6/063103

Chinese Physics C> 2017, Vol. 41> Issue(6) : 063103 DOI: 10.1088/1674-1137/41/6/063103

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

Jia-ju Zhang ^,

1.
Dipartimento di Fisica, Universita degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy

Abstract
HTML
Reference
Related

PDF

Abstract：
We calculate the contributions of a general non-vacuum conformal family to Rényi entropy in two-dimensional conformal field theory (CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by Δ. For the case of two short intervals on a complex plane, we expand the Rényi mutual information by the cross ratio x to order x^2Δ+2. For the case of one interval on a torus with low temperature, we expand the Rényi entropy by q=exp(-2πβ/L), with β being the inverse temperature and L being the spatial period, to order q^Δ+2. To make the result meaningful, we require that the scaling dimension Δ cannot be too small. For two intervals on a complex plane we need Δ >1, and for one interval on a torus we need Δ >2. We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side, and find matches of gravity and CFT results.
- R ,
- nyi entropy ,
- entanglement entropy ,
- conformal field theory

References

[1]	S. Ryu and T. Takayanagi, Phys. Rev. Lett., series 96: 181602 (2006)
[2]	P. Calabrese and J. L. Card-y, J. Stat. Mech., 0406: P06002 (2004)
[3]	S. Ryu and T. Takayanagi, JHEP, series 0608: 045 (2006)
[4]	C. G. Callan Jr. and F. Wilczek, Phys. Lett. B, series 333: 55-61 (1994)
[5]	C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B, series 424: 443-467 (1994)
[6]	J. M. Maldacena, Int. J. Theor. Phys., series 38: 1113-1133 (1999). [Adv. Theor. Math. Phys., 2: 231 (1998)].
[7]	S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B, series 428 105-114 (1998)
[8]	E. Witten, Adv. Theor. Math. Phys., series 2: 253-291 (1998)
[9]	O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Phys. Rept. series 323: 183-386 (2000)
[10]	M. Fujita, W. Li, S. Ryu, and T. Takayanagi, JHEP, series 06: 066 (2009)
[11]	M. Headrick, Phys. Rev. D, series 82: 126010 (2010)
[12]	T. Barrella, X. Dong, S. A. Hartnoll, and V. L. Martin, JHEP, series 1309: 109 (2013)
[13]	T. Faulkner, A. Lewkowycz, and J. Maldacena, JHEP, series 1311: 074 (2013)
[14]	J. D. Brown and M. Henneaux, Commun. Math. Phys., series 104: 207-226 (1986)
[15]	A. Maloney and E. Witten, JHEP, series 1002: 029 (2010)
[16]	X. Yin, Commun. Num. Theor. Phys., series 2 285-324 (2008)
[17]	S. Giombi, A. Maloney, and X. Yin, JHEP, series 0808: 007 (2008)
[18]	T. Faulkner, arXiv:1303.7221 [hep-th]
[19]	B. Chen and J.-Q. Wu, JHEP, series 08: 032 (2014)
[20]	P. Calabrese, J. Cardy, and E. Tonni, J. Stat. Mech., series 1101: P01021 (2011)
[21]	T. Hartman, arXiv:1303.6955 [hep-th]
[22]	B. Chen and J.-J. Zhang, JHEP, series 1311 164 (2013)
[23]	J. Cardy and C. P. Herzog, Phys. Rev. Lett., series 112: 171603 (2014)
[24]	B. Chen, J. Long, and J.-J. Zhang, JHEP, series 1404: 041 (2014) arXiv:1312.5510 [hep-th]
[25]	E. Perlmutter, JHEP, series 05: 052 (2014)
[26]	B. Chen, F.-Y. Song, and J.-J. Zhang, JHEP, series 1403: 137 (2014)
[27]	M. Beccaria and G. Macorini, JHEP, series 1404: 045 (2014)
[28]	J. Long, JHEP, series 12: 055 (2014)
[29]	B. Chen and J.-Q. Wu, Phys. Rev. D, series 91: 086012 (2015)
[30]	B. Chen and J.-Q. Wu, Phys. Rev. D, series 92: 126002 (2015)
[31]	B. Chen and J.-Q. Wu, Phys. Rev. D, series 92: 106001 (2015)
[32]	B. Chen, J.-Q. Wu, and Z.-C. Zheng, Phys. Rev. D, series 92: 066002 (2015)
[33]	B. Chen and J.-Q. Wu, JHEP, series 12: 109 (2015)
[34]	J.-j. Zhang, JHEP, series 1512: 027 (2015)
[35]	Z. Li and J.-J. Zhang, JHEP, series 1605: 130 (2016)
[36]	B. Chen and J.-Q. Wu, JHEP, series 07: 049 (2016)
[37]	B. Chen, J.-B. Wu, and J.-J. Zhang, JHEP, series 08: 130 (2016)
[38]	Z. Li and J.-J. Zhang, arXiv:1611.00546 [hep-th]
[39]	P. Di Francesco, P. Mathieu, and D. Senechal, (New York, USA, 1997)
[40]	R. Blumenhagen and E. Plauschinn, Lect. Notes Phys., series 779: 1-256 (2009)

[1]	N. Amangeldi , N. Burtebayev , G. Yergaliuly , Maulen Nassurlla , B. Balabekov , Abylay Tangirbergen , Awad A. Ibraheem , Mohamed A. Dewidar , Sh. Hamada . Breakup of ⁷Li in the field of ^118,120Sn nuclei and its effect on the elastic scattering channel. Chinese Physics C, 2026, 50(2): 1-12.
[2]	Renli Xu , Chen Wu , Jian Liu , Bin Hong , Jie Peng , Xiong Li , Ruxian Zhu , Zhizhen Zhao , Zhongzhou Ren . Ground-state properties of finite nuclei in relativistic Hartree-Bogoliubov theory with an improved quark mass density-dependent model. Chinese Physics C, 2026, 50(2): 1-12.
[3]	Y. P. Wang , Y. K. Wang , P. W. Zhao . Tilted-axis-cranking covariant density functional theory for the high-spin spectroscopy in ⁶⁹Ga. Chinese Physics C, 2026, 50(2): 1-5. doi: 10.1088/1674-1137/ae07b8
[4]	Minghui Ding , Fei Gao , Sebastian M. Schmidt . Anisotropic quark propagation and Zeeman effect in an external magnetic field. Chinese Physics C, 2026, 50(2): 1-19.
[5]	Alim Ruzi , Youpeng Wu , Ran Ding , Qiang Li . Searching Quantum Entanglement in pp → ZZ process. Chinese Physics C, 2026, 50(3): 1-8.
[6]	Jingxuan Chen , Xiaopeng Wang , Yanbing Cai , Xurong Chen , Qian Wang . Valence quark distributions of pions: insights from Tsallis entropy. Chinese Physics C, 2026, 50(1): 013103. doi: 10.1088/1674-1137/ae0998
[7]	Ronghao Hu , Qike Gu , Kejian Shi , Zezhong Wei , Meng Lv , Shiyang Zou , Yongkun Ding . Polarized neutron beams from polarized deuterium-tritium fusion with applications to magnetic field imaging in high-energy-density plasmas. Chinese Physics C, 2025, 49(12): 124102. doi: 10.1088/1674-1137/adec4f
[8]	Qi-Quan Li , Yu Zhang , Hoernisa Iminniyaz . Rotating and non-linear magnetic-charged black hole with an anisotropic matter field. Chinese Physics C, 2025, 49(10): 105106. doi: 10.1088/1674-1137/ade0a9
[9]	Xufen Zhang , De-Cheng Zou , Chao-Ming Zhang , Ming Zhang , Rui-Hong Yue . Perturbations of massless external fields on magnetically charged black holes in string-inspired Euler-Heisenberg theory. Chinese Physics C, 2025, 49(10): 105109. doi: 10.1088/1674-1137/ade661
[10]	BAO Ai-Dong , YAO Hai-Bo , WU Shi-Shu . Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory (QED). Chinese Physics C, 2009, 33(3): 177-180. doi: 10.1088/1674-1137/33/3/003
[11]	HU Xi-Duo , SHAO Ming-Zhu , LUO Shi-Yu , LIU Yong-Sheng , ZHU De-Hai . Average Field Idea and Single Particle Model for 2 Dimension Crystallization Beams(Ⅱ). Chinese Physics C, 2004, 28(2): 196-199.
[12]	Sa Ben-hao , Zhang Xi-zhen , Li Zhu-xia , Shi Yi-jin . A PRIMARY RESEARCH OF THE PHONON RENORMALIZATION OF NUCLEAR FIELD THEORY. Chinese Physics C, 1980, 4(3): 398-400.

Access

Get Citation

Jia-ju Zhang. Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT[J]. Chinese Physics C, 2017, 41(6): 063103. doi: 10.1088/1674-1137/41/6/063103

Jia-ju Zhang. Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT[J]. Chinese Physics C, 2017, 41(6): 063103. doi: 10.1088/1674-1137/41/6/063103 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2017-02-17

Fund

Supported by ERC Starting Grant 637844-HBQFTNCER

Article Metric

Article Views(2661)
PDF Downloads(17)
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

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

Corresponding author: Jia-ju Zhang,

1. Dipartimento di Fisica, Universita degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy

Received Date: 2017-02-17

Available Online: 2017-06-05

Fund Project: Supported by ERC Starting Grant 637844-HBQFTNCER

Abstract: We calculate the contributions of a general non-vacuum conformal family to Rényi entropy in two-dimensional conformal field theory (CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by Δ. For the case of two short intervals on a complex plane, we expand the Rényi mutual information by the cross ratio x to order x^2Δ+2. For the case of one interval on a torus with low temperature, we expand the Rényi entropy by q=exp(-2πβ/L), with β being the inverse temperature and L being the spatial period, to order q^Δ+2. To make the result meaningful, we require that the scaling dimension Δ cannot be too small. For two intervals on a complex plane we need Δ >1, and for one interval on a torus we need Δ >2. We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side, and find matches of gravity and CFT results.

HTML

Reference (40)

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

Corresponding author: Jia-ju Zhang,

HTML

目录