Shift symmetries and AdS/CFT. (English) Zbl 07744248
Summary: Massive fields on anti-de Sitter (AdS) space enjoy galileon-like shift symmetries at particular values of their masses. We explore how these shift symmetries are realized through the boundary conformal field theory (CFT), at the level of the 2-point functions. In the alternate quantization scheme in which the dual conformal field gets the smaller \(\Delta_-\) conformal dimension, the shift symmetry is realized as a gauge symmetry in the dual CFT, so that only shift invariant operators are true conformal primary fields. In the standard quantization scheme the shift symmetry acts on the source, leading to Ward identities that take the form of integral constraints.
MSC:
| 81-XX | Quantum theory |
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| [1] | Maldacena, JM, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 2, 231 (1998) · Zbl 0914.53047 · doi:10.4310/ATMP.1998.v2.n2.a1 |
| [2] | S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE]. · Zbl 1407.82005 |
| [3] | Hartnoll, SA, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav., 26 (2009) · Zbl 1181.83003 · doi:10.1088/0264-9381/26/22/224002 |
| [4] | M. Baggioli, Applied Holography: A Practical Mini-Course, M.Sc. thesis, Madrid, IFT, Spain (2019) [doi:10.1007/978-3-030-35184-7] [arXiv:1908.02667] [INSPIRE]. |
| [5] | Antonini, S.; Swingle, B., Cosmology at the end of the world, Nature Phys., 16, 881 (2020) · doi:10.1038/s41567-020-0909-6 |
| [6] | Ammon, M.; Baggioli, M.; Jiménez-Alba, A., A Unified Description of Translational Symmetry Breaking in Holography, JHEP, 09, 124 (2019) · Zbl 1423.83067 · doi:10.1007/JHEP09(2019)124 |
| [7] | Cai, R-G; Li, L.; Li, L-F; Yang, R-Q, Introduction to Holographic Superconductor Models, Sci. China Phys. Mech. Astron., 58 (2015) · doi:10.1007/s11433-015-5676-5 |
| [8] | A. Marzolla, The Ward identity of Symmetry Breaking from Holographic Renormalization, Ph.D. thesis, Université Libre de Bruxelles, PTM, Brussels, Belgium (2017) [arXiv:1712.09251] [INSPIRE]. |
| [9] | A. Marzolla, Symmetry breaking and Goldstone bosons in holographic strongly coupled field theories: Relativistic and non-relativistic examples, Ph.D. thesis, Université Libre de Bruxelles, Brussels, Belgium (2017) [INSPIRE]. |
| [10] | Bonifacio, J.; Hinterbichler, K.; Joyce, A.; Rosen, RA, Shift Symmetries in (Anti) de Sitter Space, JHEP, 02, 178 (2019) · Zbl 1411.83062 · doi:10.1007/JHEP02(2019)178 |
| [11] | Luty, MA; Porrati, M.; Rattazzi, R., Strong interactions and stability in the DGP model, JHEP, 09, 029 (2003) · doi:10.1088/1126-6708/2003/09/029 |
| [12] | Nicolis, A.; Rattazzi, R.; Trincherini, E., The Galileon as a local modification of gravity, Phys. Rev. D, 79 (2009) · doi:10.1103/PhysRevD.79.064036 |
| [13] | Cheung, C.; Kampf, K.; Novotny, J.; Trnka, J., Effective Field Theories from Soft Limits of Scattering Amplitudes, Phys. Rev. Lett., 114 (2015) · doi:10.1103/PhysRevLett.114.221602 |
| [14] | Hinterbichler, K.; Joyce, A., Hidden symmetry of the Galileon, Phys. Rev. D, 92 (2015) · doi:10.1103/PhysRevD.92.023503 |
| [15] | Cheung, C., A Periodic Table of Effective Field Theories, JHEP, 02, 020 (2017) · Zbl 1377.81123 · doi:10.1007/JHEP02(2017)020 |
| [16] | Novotny, J., Geometry of special Galileons, Phys. Rev. D, 95 (2017) · doi:10.1103/PhysRevD.95.065019 |
| [17] | Klebanov, IR; Witten, E., AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B, 556, 89 (1999) · Zbl 0958.81134 · doi:10.1016/S0550-3213(99)00387-9 |
| [18] | C. Fefferman and C.R. Graham, Conformal invariants, in Élie Cartan and today’s mathematics, Lyon France, June 25-29 (1984) [Asterisk S131, French Mathematical Society (1985)] [http://www.numdam.org/item/AST_1985___S131___95_0/]. |
| [19] | G. Mack, All unitary ray representations of the conformal group SU(2, 2) with positive energy, Commun. Math. Phys.55 (1977) 1 [INSPIRE]. · Zbl 0352.22012 |
| [20] | J.C. Jantzen, Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren, Math. Ann.226 (1977) 53. · Zbl 0372.17003 |
| [21] | Minwalla, S., Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys., 2, 783 (1998) · Zbl 1041.81534 · doi:10.4310/ATMP.1998.v2.n4.a4 |
| [22] | Osborn, H.; Petkou, AC, Implications of conformal invariance in field theories for general dimensions, Annals Phys., 231, 311 (1994) · Zbl 0795.53073 · doi:10.1006/aphy.1994.1045 |
| [23] | D.Z. Freedman, K. Johnson and J.I. Latorre, Differential regularization and renormalization: A New method of calculation in quantum field theory, Nucl. Phys. B371 (1992) 353 [INSPIRE]. |
| [24] | Petkou, A.; Skenderis, K., A Nonrenormalization theorem for conformal anomalies, Nucl. Phys. B, 561, 100 (1999) · Zbl 0958.81161 · doi:10.1016/S0550-3213(99)00514-3 |
| [25] | Bianchi, M.; Freedman, DZ; Skenderis, K., Holographic renormalization, Nucl. Phys. B, 631, 159 (2002) · Zbl 0995.81075 · doi:10.1016/S0550-3213(02)00179-7 |
| [26] | Skenderis, K., Lecture notes on holographic renormalization, Class. Quant. Grav., 19, 5849 (2002) · Zbl 1044.83009 · doi:10.1088/0264-9381/19/22/306 |
| [27] | Penedones, J.; Trevisani, E.; Yamazaki, M., Recursion Relations for Conformal Blocks, JHEP, 09, 070 (2016) · Zbl 1390.81533 · doi:10.1007/JHEP09(2016)070 |
| [28] | Brust, C.; Hinterbichler, K., Free □^kscalar conformal field theory, JHEP, 02, 066 (2017) · Zbl 1377.81158 · doi:10.1007/JHEP02(2017)066 |
| [29] | Brust, C.; Hinterbichler, K., Partially Massless Higher-Spin Theory, JHEP, 02, 086 (2017) · Zbl 1377.81062 · doi:10.1007/JHEP02(2017)086 |
| [30] | N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE]. |
| [31] | Isono, H.; Noumi, T.; Shiu, G., Momentum space approach to crossing symmetric CFT correlators, JHEP, 07, 136 (2018) · Zbl 1395.81228 · doi:10.1007/JHEP07(2018)136 |
| [32] | H. Isono, T. Noumi and G. Shiu, Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension, JHEP10 (2019) 183 [arXiv:1908.04572] [INSPIRE]. · Zbl 1427.81135 |
| [33] | Sleight, C.; Taronna, M., Bootstrapping Inflationary Correlators in Mellin Space, JHEP, 02, 098 (2020) · Zbl 1435.81174 · doi:10.1007/JHEP02(2020)098 |
| [34] | Dolan, L.; Nappi, CR; Witten, E., Conformal operators for partially massless states, JHEP, 10, 016 (2001) · doi:10.1088/1126-6708/2001/10/016 |
| [35] | Bekaert, X.; Grigoriev, M., Notes on the ambient approach to boundary values of AdS gauge fields, J. Phys. A, 46 (2013) · Zbl 1268.81110 · doi:10.1088/1751-8113/46/21/214008 |
| [36] | Bekaert, X.; Grigoriev, M., Higher order singletons, partially massless fields and their boundary values in the ambient approach, Nucl. Phys. B, 876, 667 (2013) · Zbl 1284.81188 · doi:10.1016/j.nuclphysb.2013.08.015 |
| [37] | Bekaert, X.; Grigoriev, M.; Skvortsov, ED, Higher Spin Extension of Fefferman-Graham Construction, Universe, 4, 17 (2018) · doi:10.3390/universe4020017 |
| [38] | Chekmenev, A.; Grigoriev, M., Conformal Lagrangians from the (formal) near boundary analysis of AdS gauge fields, Nucl. Phys. B, 967 (2021) · Zbl 07408622 · doi:10.1016/j.nuclphysb.2021.115403 |
| [39] | Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048 · doi:10.4310/ATMP.1998.v2.n2.a2 |
| [40] | Henningson, M.; Skenderis, K., Holography and the Weyl anomaly, Fortsch. Phys., 48, 125 (2000) · Zbl 0976.81093 · doi:10.1002/(SICI)1521-3978(20001)48:1/3<125::AID-PROP125>3.0.CO;2-B |
| [41] | Henningson, M.; Skenderis, K., The Holographic Weyl anomaly, JHEP, 07, 023 (1998) · Zbl 0958.81083 · doi:10.1088/1126-6708/1998/07/023 |
| [42] | de Haro, S.; Solodukhin, SN; Skenderis, K., Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys., 217, 595 (2001) · Zbl 0984.83043 · doi:10.1007/s002200100381 |
| [43] | Skenderis, K., Asymptotically Anti-de Sitter space-times and their stress energy tensor, Int. J. Mod. Phys. A, 16, 740 (2001) · Zbl 0982.83007 · doi:10.1142/S0217751X0100386X |
| [44] | Caldarelli, MM; Christodoulou, A.; Papadimitriou, I.; Skenderis, K., Phases of planar AdS black holes with axionic charge, JHEP, 04, 001 (2017) · Zbl 1378.83031 · doi:10.1007/JHEP04(2017)001 |
| [45] | Minces, P.; Rivelles, VO, Scalar field theory in the AdS/CFT correspondence revisited, Nucl. Phys. B, 572, 651 (2000) · Zbl 1068.81599 · doi:10.1016/S0550-3213(99)00833-0 |
| [46] | Minces, P., Multitrace operators and the generalized AdS/CFT prescription, Phys. Rev. D, 68 (2003) · doi:10.1103/PhysRevD.68.024027 |
| [47] | Rivelles, VO, Quantization in AdS and the AdS/CFT correspondence, Int. J. Mod. Phys. A, 18, 2099 (2003) · Zbl 1040.81071 · doi:10.1142/S0217751X03015544 |
| [48] | Minces, P., On the role of boundary terms in the AdS/CFT correspondence, Nucl. Phys. B Proc. Suppl., 127, 174 (2004) · doi:10.1016/S0920-5632(03)02425-3 |
| [49] | Minces, P., Bound states in the AdS/CFT correspondence, Phys. Rev. D, 70 (2004) · doi:10.1103/PhysRevD.70.025011 |
| [50] | Elitzur, S.; Giveon, A.; Porrati, M.; Rabinovici, E., Multitrace deformations of vector and adjoint theories and their holographic duals, JHEP, 02, 006 (2006) · doi:10.1088/1126-6708/2006/02/006 |
| [51] | Hartman, T.; Rastelli, L., Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP, 01, 019 (2008) · doi:10.1088/1126-6708/2008/01/019 |
| [52] | M. Porrati and C.C.Y. Yu, Notes on Relevant, Irrelevant, Marginal and Extremal Double Trace Perturbations, JHEP11 (2016) 040 [arXiv:1609.00353] [INSPIRE]. · Zbl 1390.81536 |
| [53] | Bzowski, A.; McFadden, P.; Skenderis, K., Implications of conformal invariance in momentum space, JHEP, 03, 111 (2014) · Zbl 1406.81082 · doi:10.1007/JHEP03(2014)111 |
| [54] | Bzowski, A.; McFadden, P.; Skenderis, K., Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies, JHEP, 03, 066 (2016) · doi:10.1007/JHEP03(2016)066 |
| [55] | A. Bzowski, Dimensional renormalization in AdS/CFT, arXiv:1612.03915 [INSPIRE]. |
| [56] | Bzowski, A.; McFadden, P.; Skenderis, K., A handbook of holographic 4-point functions, JHEP, 12, 039 (2022) · Zbl 1536.81064 · doi:10.1007/JHEP12(2022)039 |
| [57] | 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. D58 (1998) 106006 [hep-th/9805145] [INSPIRE]. |
| [58] | Marolf, D.; Ross, SF, Boundary Conditions and New Dualities: Vector Fields in AdS/CFT, JHEP, 11, 085 (2006) · doi:10.1088/1126-6708/2006/11/085 |
| [59] | Kabat, D.; Lifschytz, G.; Roy, S.; Sarkar, D., Holographic representation of bulk fields with spin in AdS/CFT, Phys. Rev. D, 86 (2012) · doi:10.1103/PhysRevD.86.026004 |
| [60] | Bonifacio, J.; Hinterbichler, K.; Joyce, A.; Roest, D., Exceptional scalar theories in de Sitter space, JHEP, 04, 128 (2022) · Zbl 1522.81461 · doi:10.1007/JHEP04(2022)128 |
| [61] | Armstrong, C.; Lipstein, A.; Mei, J., Enhanced soft limits in de Sitter space, JHEP, 12, 064 (2022) · Zbl 1536.81114 · doi:10.1007/JHEP12(2022)064 |
| [62] | De Rham, C.; Hinterbichler, K.; Johnson, LA, On the (A)dS Decoupling Limits of Massive Gravity, JHEP, 09, 154 (2018) · Zbl 1398.83093 · doi:10.1007/JHEP09(2018)154 |
| [63] | Bonifacio, J.; Hinterbichler, K.; Johnson, LA; Joyce, A., Shift-Symmetric Spin-1 Theories, JHEP, 09, 029 (2019) · Zbl 1423.83050 · doi:10.1007/JHEP09(2019)029 |
| [64] | de Rham, C.; Gabadadze, G.; Tolley, AJ, Resummation of Massive Gravity, Phys. Rev. Lett., 106 (2011) · doi:10.1103/PhysRevLett.106.231101 |
| [65] | Cheung, C., On-Shell Recursion Relations for Effective Field Theories, Phys. Rev. Lett., 116 (2016) · doi:10.1103/PhysRevLett.116.041601 |
| [66] | Elvang, H.; Hadjiantonis, M.; Jones, CRT; Paranjape, S., Soft Bootstrap and Supersymmetry, JHEP, 01, 195 (2019) · Zbl 1409.81146 · doi:10.1007/JHEP01(2019)195 |
| [67] | Bittermann, N.; Joyce, A., Soft limits of the wavefunction in exceptional scalar theories, JHEP, 03, 092 (2023) · Zbl 07690656 · doi:10.1007/JHEP03(2023)092 |
| [68] | Assassi, V.; Baumann, D.; Green, D., On Soft Limits of Inflationary Correlation Functions, JCAP, 11, 047 (2012) · doi:10.1088/1475-7516/2012/11/047 |
| [69] | Hinterbichler, K.; Hui, L.; Khoury, J., An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology, JCAP, 01, 039 (2014) · doi:10.1088/1475-7516/2014/01/039 |
| [70] | Green, D.; Huang, Y.; Shen, C-H, Inflationary Adler conditions, Phys. Rev. D, 107 (2023) · doi:10.1103/PhysRevD.107.043534 |
| [71] | Conlon, JP; Ning, S.; Revello, F., Exploring the holographic Swampland, JHEP, 04, 117 (2022) · Zbl 1522.83284 · doi:10.1007/JHEP04(2022)117 |
| [72] | Apers, F.; Conlon, JP; Ning, S.; Revello, F., Integer conformal dimensions for type IIa flux vacua, Phys. Rev. D, 105 (2022) · doi:10.1103/PhysRevD.105.106029 |
| [73] | Plauschinn, E., Mass spectrum of type IIB flux compactifications — comments on AdS vacua and conformal dimensions, JHEP, 02, 257 (2023) · Zbl 1541.81140 · doi:10.1007/JHEP02(2023)257 |
| [74] | Apers, F., Aspects of AdS flux vacua with integer conformal dimensions, JHEP, 05, 040 (2023) · Zbl 07701855 · doi:10.1007/JHEP05(2023)040 |
| [75] | Hinterbichler, K., Shift symmetries for p-forms and mixed symmetry fields on (A)dS, JHEP, 11, 015 (2022) · Zbl 1536.81110 · doi:10.1007/JHEP11(2022)015 |
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