Abstract
We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the massesof higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Hikida, The masses of higher spin fields on AdS 4 and conformal perturbation theory, Phys. Rev. D 94 (2016) 026004 [arXiv:1601.01784] [INSPIRE].
Y. Hikida and T. Wada, Anomalous dimensions of higher spin currents in large-N CFTs, JHEP 01 (2017) 032 [arXiv:1610.05878] [INSPIRE].
D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10 (1974) 3235 [INSPIRE].
M. Moshe and J. Zinn-Justin, Quantum field theory in the large-N limit: a review, Phys. Rept. 385 (2003) 69 [hep-th/0306133] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: star product and AdS space, hep-th/9910096 [INSPIRE].
M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS d , Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
R.G. Leigh and A.C. Petkou, Holography of the N = 1 higher spin theory on AdS 4, JHEP 06 (2003) 011 [hep-th/0304217] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
D.J. Gross, High-energy symmetries of string theory, Phys. Rev. Lett. 60 (1988) 1229 [INSPIRE].
S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia and X. Yin, Chern-Simons theory with vector fermion matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, D = 3 bosonic vector models coupled to Chern-Simons gauge theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
S. Giombi, V. Gurucharan, V. Kirilin, S. Prakash and E. Skvortsov, On the higher-spin spectrum in large-N Chern-Simons vector models, JHEP 01 (2017) 058 [arXiv:1610.08472] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
T. Muta and D.S. Popovic, Anomalous dimensions of composite operators in the Gross-Neveu model in two + ϵ dimensions, Prog. Theor. Phys. 57 (1977) 1705 [INSPIRE].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ triality: from higher spin fields to strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [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].
S. Giombi and X. Yin, On higher spin gauge theory and the critical O(N) model, Phys. Rev. D 85 (2012) 086005 [arXiv:1105.4011] [INSPIRE].
T. Creutzig and Y. Hikida, Higgs phenomenon for higher spin fields on AdS 3, JHEP 10 (2015) 164 [arXiv:1506.04465] [INSPIRE].
D. Anselmi, Higher spin current multiplets in operator product expansions, Class. Quant. Grav. 17 (2000) 1383 [hep-th/9906167] [INSPIRE].
M.R. Gaberdiel, C. Peng and I.G. Zadeh, Higgsing the stringy higher spin symmetry, JHEP 10 (2015) 101 [arXiv:1506.02045] [INSPIRE].
K. Diab, L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, On C J and C T in the Gross-Neveu and O(N) models, J. Phys. A 49 (2016) 405402 [arXiv:1601.07198] [INSPIRE].
K. Lang and W. Rühl, The critical O(N) σ-model at dimensions 2 < d < 4: fusion coefficients and anomalous dimensions, Nucl. Phys. B 400 (1993) 597 [INSPIRE].
E.D. Skvortsov, On (un)broken higher-spin symmetry in vector models, in Proceedings, International Workshop on Higher Spin Gauge Theories, Singapore, 4–6 November 2015, pg. 103 [arXiv:1512.05994] [INSPIRE].
S. Giombi and V. Kirilin, Anomalous dimensions in CFT with weakly broken higher spin symmetry, JHEP 11 (2016) 068 [arXiv:1601.01310] [INSPIRE].
A.N. Manashov and E.D. Skvortsov, Higher-spin currents in the Gross-Neveu model at 1/n 2, JHEP 01 (2017) 132 [arXiv:1610.06938] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT d /AdS d+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
T. Kawano and K. Okuyama, Spinor exchange in AdS d+1, Nucl. Phys. B 565 (2000) 427 [hep-th/9905130] [INSPIRE].
O. Aharony, M. Berkooz and B. Katz, Non-local effects of multi-trace deformations in the AdS/CFT correspondence, JHEP 10 (2005) 097 [hep-th/0504177] [INSPIRE].
Y. Hikida and P.B. Rønne, Marginal deformations and the Higgs phenomenon in higher spin AdS 3 holography, JHEP 07 (2015) 125 [arXiv:1503.03870] [INSPIRE].
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B 431 (1998) 63 [hep-th/9803251] [INSPIRE].
W. Mueck and K.S. Viswanathan, Conformal field theory correlators from classical field theory on anti-de Sitter space. 2. Vector and spinor fields, Phys. Rev. D 58 (1998) 106006 [hep-th/9805145] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Large N = 4 holography, JHEP 09 (2013) 036 [arXiv:1305.4181] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Higher spins and strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Ronne, Extended higher spin holography and Grassmannian models, JHEP 11 (2013) 038 [arXiv:1306.0466] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Ronne, Higher spin AdS 3 holography with extended supersymmetry, JHEP 10 (2014) 163 [arXiv:1406.1521] [INSPIRE].
S. Gwak, E. Joung, K. Mkrtchyan and S.-J. Rey, Rainbow vacua of colored higher-spin (A)dS 3 gravity, JHEP 05 (2016) 150 [arXiv:1511.05975] [INSPIRE].
L. Girardello, M. Porrati and A. Zaffaroni, 3D interacting CFTs and generalized Higgs phenomenon in higher spin theories on AdS, Phys. Lett. B 561 (2003) 289 [hep-th/0212181] [INSPIRE].
A.N. Vasiliev and M. Yu. Nalimov, Analog of dimensional regularization for calculation of the renormalization group functions in the 1/n expansion for arbitrary dimension of space, Theor. Math. Phys. 55 (1983) 423 [Teor. Mat. Fiz. 55 (1983) 163] [INSPIRE].
A.N. Vasiliev and A.S. Stepanenko, A method of calculating the critical dimensions of composite operators in the massless nonlinear σ-model, Theor. Math. Phys. 94 (1993) 471 [Teor. Mat. Fiz. 95 (1993) 160] [INSPIRE].
S.E. Derkachov and A.N. Manashov, The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion, Nucl. Phys. B 522 (1998) 301 [hep-th/9710015] [INSPIRE].
M. Günaydin, E.D. Skvortsov and T. Tran, Exceptional F(4) higher-spin theory in AdS 6 at one-loop and other tests of duality, JHEP 11 (2016) 168 [arXiv:1608.07582] [INSPIRE].
S. Giombi, I.R. Klebanov and Z.M. Tan, The ABC of higher-spin AdS/CFT, arXiv:1608.07611 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1701.03563
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Hikida, Y., Wada, T. Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry. J. High Energ. Phys. 2017, 47 (2017). https://doi.org/10.1007/JHEP03(2017)047
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2017)047