Abstract
We study mass-type surface defects in a free scalar and Wilson-Fisher (WF) O(N) theories. We obtain exact results for the free scalar defect, including its RG flow and defect Weyl anomaly. We classify phases of such defects at the WF fixed point near four dimensions, whose perturbative RG flow is investigated. We propose an IR effective action for the non-perturbative regime and check its self-consistency.
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D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
K. Roumpedakis, S. Seifnashri and S.-H. Shao, Higher Gauging and Non-invertible Condensation Defects, Commun. Math. Phys. 401 (2023) 3043 [arXiv:2204.02407] [INSPIRE].
O. Aharony et al., Phases of Wilson Lines in Conformal Field Theories, Phys. Rev. Lett. 130 (2023) 151601 [arXiv:2211.11775] [INSPIRE].
S. Gukov and E. Witten, Gauge Theory, Ramification, And The Geometric Langlands Program, hep-th/0612073 [INSPIRE].
N. Drukker, J. Gomis and S. Matsuura, Probing N = 4 SYM With Surface Operators, JHEP 10 (2008) 048 [arXiv:0805.4199] [INSPIRE].
S. Gukov and E. Witten, Rigid Surface Operators, Adv. Theor. Math. Phys. 14 (2010) 87 [arXiv:0804.1561] [INSPIRE].
Y. Wang, Taming defects in \( \mathcal{N} \) = 4 super-Yang-Mills, JHEP 08 (2020) 021 [arXiv:2003.11016] [INSPIRE].
C.P. Herzog and A. Shrestha, Conformal surface defects in Maxwell theory are trivial, JHEP 08 (2022) 282 [arXiv:2202.09180] [INSPIRE].
E. Lauria, P. Liendo, B.C. Van Rees and X. Zhao, Line and surface defects for the free scalar field, JHEP 01 (2021) 060 [arXiv:2005.02413] [INSPIRE].
A. Krishnan and M.A. Metlitski, A plane defect in the 3d O(N) model, arXiv:2301.05728 [INSPIRE].
T.W. Burkhardt and J.L. Cardy, Surface critical behaviour and local operators with boundary-induced critical profiles, J. Phys. A 20 (1987) L233.
D.M. McAvity and H. Osborn, Conformal field theories near a boundary in general dimensions, Nucl. Phys. B 455 (1995) 522 [cond-mat/9505127] [INSPIRE].
K. Ohno and Y. Okabe, The 1/n expansion for the n-vector model in the semi-infinite space, Prog. Theor. Phys. 70 (1983) 1226 [INSPIRE].
T. Dimofte, D. Gaiotto and N.M. Paquette, Dual boundary conditions in 3d SCFT’s, JHEP 05 (2018) 060 [arXiv:1712.07654] [INSPIRE].
M.A. Metlitski, Boundary criticality of the O(N) model in d = 3 critically revisited, SciPost Phys. 12 (2022) 131 [arXiv:2009.05119] [INSPIRE].
G. Cuomo, Z. Komargodski, M. Mezei and A. Raviv-Moshe, Spin impurities, Wilson lines and semiclassics, JHEP 06 (2022) 112 [arXiv:2202.00040] [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].
Y. Wang, Surface defect, anomalies and b-extremization, JHEP 11 (2021) 122 [arXiv:2012.06574] [INSPIRE].
T. Shachar, R. Sinha and M. Smolkin, RG flows on two-dimensional spherical defects, arXiv:2212.08081 [INSPIRE].
M. Henningson and K. Skenderis, Weyl anomaly for Wilson surfaces, JHEP 06 (1999) 012 [hep-th/9905163] [INSPIRE].
A. Schwimmer and S. Theisen, Entanglement Entropy, Trace Anomalies and Holography, Nucl. Phys. B 801 (2008) 1 [arXiv:0802.1017] [INSPIRE].
C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [hep-th/9901021] [INSPIRE].
Y.J. Deng, H.W.J. Blöte and M.P. Nightingale, Surface and bulk transitions in three-dimensional O(n) models, Phys. Rev. E 72 (2005) 016128 [cond-mat/0504173] [INSPIRE].
Y. Deng, Bulk and surface phase transitions in the three-dimensional O(4) spin model, Phys. Rev. E 73 (2006) 056116 [INSPIRE].
F. Parisen Toldin, Boundary Critical Behavior of the Three-Dimensional Heisenberg Universality Class, Phys. Rev. Lett. 126 (2021) 135701 [arXiv:2012.00039] [INSPIRE].
M. Hu, Y. Deng and J.-P. Lv, Extraordinary-Log Surface Phase Transition in the Three-Dimensional XY Model, Phys. Rev. Lett. 127 (2021) 120603 [arXiv:2104.05152] [INSPIRE].
F.P. Toldin and M.A. Metlitski, Boundary Criticality of the 3D O(N) Model: From Normal to Extraordinary, Phys. Rev. Lett. 128 (2022) 215701 [arXiv:2111.03613] [INSPIRE].
J. Padayasi et al., The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap, SciPost Phys. 12 (2022) 190 [arXiv:2111.03071] [INSPIRE].
S. Giombi and B. Liu, Notes on a Surface Defect in the O(N) Model, arXiv:2305.11402 [INSPIRE].
M. Trépanier, Surface defects in the O(N) model, arXiv:2305.10486 [INSPIRE].
K.G. Wilson and J.B. Kogut, The renormalization group and the ε expansion, Phys. Rept. 12 (1974) 75 [INSPIRE].
G. Cuomo, Z. Komargodski and M. Mezei, Localized magnetic field in the O(N) model, JHEP 02 (2022) 134 [arXiv:2112.10634] [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].
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].
I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-Theorem without Supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
C.R. Graham, Volume and area renormalizations for conformally compact Einstein metrics, Rend. Circ. Mat. Palermo S 63 (2000) 31 [math/9909042] [INSPIRE].
P. Dey, T. Hansen and M. Shpot, Operator expansions, layer susceptibility and two-point functions in BCFT, JHEP 12 (2020) 051 [arXiv:2006.11253] [INSPIRE].
M.A. Shpot, Boundary conformal field theory at the extraordinary transition: The layer susceptibility to O(ε), JHEP 01 (2021) 055 [arXiv:1912.03021] [INSPIRE].
P.H. Ginsparg, Applied conformal field theory, hep-th/9108028 [INSPIRE].
S.K. Kehrein, The spectrum of critical exponents in (ϕ2)2 in two-dimensions theory in d = 4 − ϵ dimensions: Resolution of degeneracies and hierarchical structures, Nucl. Phys. B 453 (1995) 777 [hep-th/9507044] [INSPIRE].
J. Henriksson, The critical O(N) CFT: Methods and conformal data, Phys. Rept. 1002 (2023) 1 [arXiv:2201.09520] [INSPIRE].
Z. Komargodski and D. Simmons-Duffin, The Random-Bond Ising Model in 2.01 and 3 Dimensions, J. Phys. A 50 (2017) 154001 [arXiv:1603.04444] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
G. Cuomo, M. Mezei and A. Raviv-Moshe, Boundary conformal field theory at large charge, JHEP 10 (2021) 143 [arXiv:2108.06579] [INSPIRE].
J. Zinn-Justin, Quantum field theory and critical phenomena, vol. 171, Oxford University Press (2021).
G. Cuomo and S. Zhang, Spontaneous symmetry breaking on surface defects, arXiv:2306.00085 [INSPIRE].
T. Nishioka and Y. Sato, Free energy and defect C-theorem in free scalar theory, JHEP 05 (2021) 074 [arXiv:2101.02399] [INSPIRE].
E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in Strings, Branes and Extra Dimensions: TASI 2001, World Scientific (2004), p. 3–159.
P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CFTd, JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].
D. Gaiotto, D. Mazac and M.F. Paulos, Bootstrapping the 3d Ising twist defect, JHEP 03 (2014) 100 [arXiv:1310.5078] [INSPIRE].
A. Nahum, P. Serna, A.M. Somoza and M. Ortuño, Loop models with crossings, Phys. Rev. B 87 (2013) 184204 [arXiv:1303.2342] [INSPIRE].
Acknowledgments
We thank G. Cuomo, L. Iliesiu, Z. Komargodski, L. Rastelli, and S. Shao for many useful discussions. We are particularly grateful to G. Cuomo and Z. Komargodski for providing comments on a preliminary version of this manuscript. ARM is supported by the Simons Center for Geometry and Physics. ARM is an awardee of the Women’s Postdoctoral Career Development Award.
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Raviv-Moshe, A., Zhong, S. Phases of surface defects in Scalar Field Theories. J. High Energ. Phys. 2023, 143 (2023). https://doi.org/10.1007/JHEP08(2023)143
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DOI: https://doi.org/10.1007/JHEP08(2023)143