Abstract
We study a class of renormalization group flows on line defects that can be described by a generalized free field with ordered planar contractions on the line. They are realized, for example, in large N gauge theories with matter in the fundamental representation and arise generically in non-relativistic CFTs. We analyze the flow exactly and compute the change in the g-function between the UV and IR fixed points. We relate the result to the change in the two-point function of the displacement operator and check the monotonicity of the defect entropy along the flow analytically. Finally, we give a general realization of this type of flow starting from the direct sum of the IR fixed point and a trivial line. This type of defect renormalization group flow parallels the well-studied case of double-trace flow.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
A. Söderberg Rousu, Defects, renormalization and conformal field theory, Ph.D. thesis, Uppsala U., Uppsala, Sweden (2023) [INSPIRE].
G. Cuomo, Z. Komargodski and A. Raviv-Moshe, Renormalization group flows on line defects, Phys. Rev. Lett. 128 (2022) 021603 [arXiv:2108.01117] [INSPIRE].
I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
P. Dorey, I. Runkel, R. Tateo and G. Watts, g function flow in perturbed boundary conformal field theories, Nucl. Phys. B 578 (2000) 85 [hep-th/9909216] [INSPIRE].
S. Yamaguchi, Holographic RG flow on the defect and g theorem, JHEP 10 (2002) 002 [hep-th/0207171] [INSPIRE].
D. Friedan and A. Konechny, On the boundary entropy of one-dimensional quantum systems at low temperature, Phys. Rev. Lett. 93 (2004) 030402 [hep-th/0312197] [INSPIRE].
T. Azeyanagi, A. Karch, T. Takayanagi and E.G. Thompson, Holographic calculation of boundary entropy, JHEP 03 (2008) 054 [arXiv:0712.1850] [INSPIRE].
T. Takayanagi, Holographic dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
J. Estes et al., On holographic defect entropy, JHEP 05 (2014) 084 [arXiv:1403.6475] [INSPIRE].
D. Gaiotto, Boundary F-maximization, arXiv:1403.8052 [INSPIRE].
K. Jensen and A. O’Bannon, Constraint on defect and boundary renormalization group flows, Phys. Rev. Lett. 116 (2016) 091601 [arXiv:1509.02160] [INSPIRE].
H. Casini, I. Salazar Landea and G. Torroba, The g-theorem and quantum information theory, JHEP 10 (2016) 140 [arXiv:1607.00390] [INSPIRE].
N. Andrei et al., Boundary and defect CFT: open problems and applications, J. Phys. A 53 (2020) 453002 [arXiv:1810.05697] [INSPIRE].
N. Kobayashi, T. Nishioka, Y. Sato and K. Watanabe, Towards a C-theorem in defect CFT, JHEP 01 (2019) 039 [arXiv:1810.06995] [INSPIRE].
H. Casini, I. Salazar Landea and G. Torroba, Irreversibility in quantum field theories with boundaries, JHEP 04 (2019) 166 [arXiv:1812.08183] [INSPIRE].
S. Giombi and H. Khanchandani, CFT in AdS and boundary RG flows, JHEP 11 (2020) 118 [arXiv:2007.04955] [INSPIRE].
Y. Wang, Surface defect, anomalies and b-extremization, JHEP 11 (2021) 122 [arXiv:2012.06574] [INSPIRE].
T. Nishioka and Y. Sato, Free energy and defect C-theorem in free scalar theory, JHEP 05 (2021) 074 [arXiv:2101.02399] [INSPIRE].
Y. Wang, Defect a-theorem and a-maximization, JHEP 02 (2022) 061 [arXiv:2101.12648] [INSPIRE].
Y. Sato, Free energy and defect C-theorem in free fermion, JHEP 05 (2021) 202 [arXiv:2102.11468] [INSPIRE].
S. Giombi, V. Kirilin and E. Perlmutter, Double-trace deformations of conformal correlations, JHEP 02 (2018) 175 [arXiv:1801.01477] [INSPIRE].
S.S. Gubser and I.R. Klebanov, A universal result on central charges in the presence of double trace deformations, Nucl. Phys. B 656 (2003) 23 [hep-th/0212138] [INSPIRE].
T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP 01 (2008) 019 [hep-th/0602106] [INSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions, and AdS / CFT correspondence, hep-th/0112258 [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
S. Giombi et al., AdS description of induced higher-spin gauge theory, JHEP 10 (2013) 016 [arXiv:1306.5242] [INSPIRE].
M. Billó et al., Line defects in the 3d Ising model, JHEP 07 (2013) 055 [arXiv:1304.4110] [INSPIRE].
B. Gabai, A. Sever and D.-L. Zhong, Line operators in Chern-Simons-matter theories and bosonization in three dimensions, Phys. Rev. Lett. 129 (2022) 121604 [arXiv:2204.05262] [INSPIRE].
B. Gabai, A. Sever and D.-L. Zhong, Line operators in Chern-Simons-matter theories and bosonization in three dimensions. Part II. Perturbative analysis and all-loop resummation, JHEP 04 (2023) 070 [arXiv:2212.02518] [INSPIRE].
H.J. Haubold, A.M. Mathai and R.K. Saxena, Mittag-Leffler functions and their applications, arXiv:0909.0230.
O. Aharony et al., Phases of Wilson lines in conformal field theories, Phys. Rev. Lett. 130 (2023) 151601 [arXiv:2211.11775] [INSPIRE].
O. Aharony et al., Phases of Wilson lines: conformality and screening, JHEP 12 (2023) 183 [arXiv:2310.00045] [INSPIRE].
B. Gabai, A. Sever and D.-L. Zhong, Bootstrapping smooth conformal defects in Chern-Simons-matter theories, JHEP 03 (2024) 055 [arXiv:2312.17132] [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in N = 4 super Yang Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].
Acknowledgments
We thank Z. Komargodski, I. Klebanov, and S. Yankielowicz, for valuable discussions and comments on the manuscript. AS thanks the Simons Center for Geometry and Physics for its hospitality. IN thanks Z. Bajnok and Eötvös Loránd University for their warm hospitality. AS is supported by the Israel Science Foundation, grant number 1197/20. DlZ is supported in part by the Royal Society University Research Fellowships grant URF/R1/221310 “Bootstrapping Quantum Gravity”.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2404.07290
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Nagar, I., Sever, A. & Zhong, Dl. Planar RG flows on line defects. J. High Energ. Phys. 2024, 110 (2024). https://doi.org/10.1007/JHEP06(2024)110
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2024)110