A Consistent Truncation of 11D Supergravity, (pseudo)Scalars in AdS_4 Space and Exact Dual Solutions in the Boundary 3D Field Theory

Naghdi, Mohammad

doi:10.61882/jmrph.7.2.21

A Consistent Truncation of 11D Supergravity, (pseudo)Scalars in AdS_4 Space and Exact Dual Solutions in the Boundary 3D Field Theory

Author

Mohammad Naghdi

University of Ilam

https://doi.org/10.61882/jmrph.7.2.21

Abstract

Starting from 11-dimensional supergravity over AdS_4×CP^3⋉S^1/Z_k and adding a new 4-form field-strength, we get a consistent Kaluza-Klein reduction. In fact, the resulting SU(4)×U(1)-singlet (pseudo)scalars in the 4-dimensional Euclidean anti-de Sitter space arise from probe (anti)M-branes wrapped around directions of the internal space, in the (Wick-rotated) skew-whiffed background; and the resulting anti-M2-branes theory breaks all supersymmetries and parity of the original theory. In addition, the bulk (scalar) equations and solutions break the scale-invariance. Taking the backreaction on the external and internal spaces, the resulting equations correspond to exactly marginal (Δ_+=3) and marginally irrelevant boundary operators. Presenting exact solutions for the equation when taking the backreaction and solving the main bulk equation in probe approximation for the massless (m^2=0) and a massive (m^2=40) mode with math methods and especially the Adomian decomposition method, we get perturbative solutions appropriate for near the boundary analyzes. Such solutions have at least the SO(4) symmetry and present instantons responsible for tunnelling among almost degenerate vacua of the Higgs-like scalar potential or true-vacuum bubbles growing from the false vacuum in the form of bounce solutions. To realize the bulk symmetries and in particular supersymmetry breaking, we swap the three fundamental representations of SO(8) for gravitino and as a result, we realize the desired singlet (pseudo)scalars in the spectrum. As the same way, by focusing on the U(1)×U(1) part of the original quiver gauge group of the 3-dimensional boundary Chern-Simons-matter (ABJM) theory, taking just a single boundary scalar and a single fermion, introducing various marginal and irrelevant (Δ_+=8) boundary operators and deforming the boundary action with them, we finally arrive at exact solutions with finite actions which are in fact small instantons on a three-sphere at infinity. In addition, using the AdS_4/CFT_3 duality rules, we confirm the state-operator correspondence in the leading order and match elements of the bulk and boundary solutions.

Keywords

11-Dimensional supergravity

Consistent truncation

(pseudo)Scalars in AdS_4 space

Adomian decomposition method

AdS_4/CFT_3 correspondence

Dual boundary operators

Instantons

M. Naghdi, "A truncation of 11-dimensional supergravity for Fubini-like instantons in AdS_4/CFT_3", Fortschr. Phys. 67, 1800044 (2018), [arXiv:1708.02530 [hep-th]]. [DOI:10.1002/prop.201800044]

M. Naghdi, "Instantons in AdS_4 from (anti)membranes wrapping S^7to Bose-Fermi duality in CFT_3's", Eur. Phys. J. Plus 138, 45 (2023), [arXiv:2002.06547 [hep-th]]. [DOI:10.1140/epjp/s13360-023-03686-y]

M. Naghdi, "Solutions for scalar equations in AdS_4 with Adomian method and boundary CFT_3 duals", Eur. Phys. J. Plus 138, 300 (2023), [arXiv:2005.00358 [hep-th]]. [DOI:10.1140/epjp/s13360-023-03905-6]

محمد نقدی، " جواب‌های اینستنتونی در مدلی از تناظر AdS_٤/CFT_٣ "، مجله پژوهش فیزیک ایران، جلد ٢٠، شمـاره ٣، صفحه ٤٧١، پاییز ١٣٩٩.

M. Naghdi, "Higgs-like (pseudo)Scalars in AdS_4, Marginal and Irrelevant Deformations in CFT_3 and Instantons on S^3 ", Chin. Phys. C 48, 043104 (2024), [arXiv:2311.11671 [hep-th]]. [DOI:10.1088/1674-1137/ad205f]

O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, "N=6 superconformal Chern-Simons matter theories, M2-branes and their gravity duals", JHEP 0810, 091 (2008), [arXiv:0806.1218 [hep-th]]. [DOI:10.1088/1126-6708/2008/10/091]

G. Adomian, "Solving frontier problems of physics: The decomposition method", Springer, 1st Edition (1994). [DOI:10.1007/978-94-015-8289-6_1]

E. Bergshoeff, M. de Roo, E. Eyras, B. Janssen and J. P. van der Schaar, "Multiple intersections of D-branes and M-branes,", Nucl. Phys. B 494, 119 (1997), [arXiv:hep-th/9612095]. [DOI:10.1016/S0550-3213(97)00151-X]

S. R. Coleman and F. De Luccia, "Gravitational effects on and of vacuum decay", Phys. Rev. D 21, 3305 (1980). [DOI:10.1103/PhysRevD.21.3305]

L. F. Abbott and S. Coleman, "The collapse of an anti-de Sitter bubble", Nucl. Phys. B 259, 4170 (1985). [DOI:10.1016/0550-3213(85)90305-0]

F. C. Adams, "General solutions for tunneling of scalar fields with quartic potentials", Phys. Rev. D 48, 2800 (1993), [arXiv:hep-ph/9302321]. [DOI:10.1103/PhysRevD.48.2800] [PMID]

E. Witten, "Anti-de Sitter space and holography", Adv. Theor. Math. Phys. 2, 253 (1998), [arXiv:hep-th/9802150]. [DOI:10.4310/ATMP.1998.v2.n2.a2]

D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, "Correlation functions in the CFT_d/AdS_(d+1) correpondence", Nucl. Phys. B 546, 96 (1999), [arXiv:hep-th/9804058]. [DOI:10.1016/S0550-3213(99)00053-X]

A.-M. Wazwaz, "Partial Differential Equations and Solitary Waves Theory", Springer, 1nd Edition (2009). [DOI:10.1007/978-3-642-00251-9]

M. Naghdi, "Non-Minimally Coupled Pseudoscalars in AdS_4 for Instantons in CFT_3", Class. Quant. Grav. 33, 115005 (2016), [arXiv:1505.00179 [hep-th]]. [DOI:10.1088/0264-9381/33/11/115005]

M. J. Duff, B. E. W. Nilsson and C. N. Pope, "Superunification from eleven dimensions", Nucl. Phys. B 233, 433 (1984). [DOI:10.1016/0550-3213(84)90577-7]

D. N. Page and C. N. Pope, "Instabilities in Englert-type supergravity solutions", Phys. Lett. B 145, 333 (1984). [DOI:10.1016/0370-2693(84)90055-8]

J. P. Gauntlett, S. Kim, O. Varela and D. Waldram, "Consistent supersymmetric Kaluza-Klein truncations with massive modes", JHEP 0904, 102 (2009), [arXiv:0901.0676 [hep-th]]. [DOI:10.1088/1126-6708/2009/04/102]

S. Fubini, "A new approach to conformal invariant field theories", Nuovo Cim. A 34, 521 (1976). [DOI:10.1007/BF02785664]

M. Naghdi, "Massive (pesudo)scalars in AdS_4, SO(4) invariant solutions and holography", Eur. Phys. J. Plus 133, 307 (2018), [arXiv:1703.02765 [hep-th]]. [DOI:10.1140/epjp/i2018-12121-0]

M. J. Duff, B. E. W. Nilsson and C. N. Pope, "Kaluza-Klein Supergravity", Phys. Rept. 130, 1 (1986). [DOI:10.1016/0370-1573(86)90163-8]

M. Bianchi, R. Poghossian and M. Samsonyan, "Precision spectroscopy and higher spin symmetry in the ABJM model", JHEP 1010, 021 (2010), [arXiv:1005.5307 [hep-th]]. [DOI:10.1007/JHEP10(2010)021]

I. Bena, "The M theory dual of a three-dimensional theory with reduced supersymmetry", Phys. Rev. D 62, 126006 (2000), [arXiv:hep-th/0004142]. [DOI:10.1103/PhysRevD.62.126006]

O. Aharony, O. Bergman, D. L. Jafferis, "Fractional M2-branes", JHEP 0811, 043 (2008), [arXiv:0807.4924 [hep-th]]. [DOI:10.1088/1126-6708/2008/11/043]

X. Chu, H. Nastase, B. Nilsson and C. Papageorgakis, "Higgsing M2 to D2 with gravity: N=6 chiral supergravity from topologically gauged ABJM theory", JHEP 1104, 040 (2011), [arXiv:1012.5969 [hep-th]]. [DOI:10.1007/JHEP04(2011)040]

P. Breitenlohner and D. Z. Freedman, "Positive energy in anti-de Sitter backgrounds and gauged extended supergravity", Phys. Lett. B 115, 197 (1982). [DOI:10.1016/0370-2693(82)90643-8]

V. Balasubramanian, P. Kraus and A. Lawrence, "Bulk vs boundary dynamics in anti-de Sitter spacetime", Phys. Rev. D 59, 046003 (1999), [arXiv:hep-th/9805171]. [DOI:10.1103/PhysRevD.59.046003]

I. R. Klebanov and E. Witten, "AdS/CFT correspondence and symmetry breaking", Nucl. Phys. B 556, 89 (1999), [arXiv:hep-th/9905104]. [DOI:10.1016/S0550-3213(99)00387-9]

S. Terashima, "On M5-branes in N=6 membrane action", JHEP 0808, 080 (2008), [arXiv:0807.0197 [hep-th]]. [DOI:10.1088/1126-6708/2008/08/080]

M. Naghdi, "New instantons in AdS_4/CFT_3 from D4-branes wrapping some of CP^3", Phys. Rev. D 88, 026013 (2013), [arXiv:1302.5294 [hep-th]]. [DOI:10.1103/PhysRevD.88.026013]

M. Naghdi, "Marginal fluctuations as instantons on M2/D2-branes", Eur. Phys. J. C 74, 2826 (2014), [arXiv:1302.5534 [hep-th]]. [DOI:10.1140/epjc/s10052-014-2826-2]

M. Naghdi, "Dual localized objects from M-branes over AdS_4×S^7/Z_k", Class. Quant. Grav. 32, 215018 (2015), [arXiv:1502.03281 [hep-th]]. [DOI:10.1088/0264-9381/32/21/215018]

N. Seiberg and E. Witten, "String theory and noncommutative geometry", JHEP 9909, 032 (1999), [arXiv:hep-th/9908142]. [DOI:10.1088/1126-6708/1999/09/032]

Sh. Minwalla and Sh. Yokoyama, "Chern Simons Bosonization along RG Flows", JHEP 1602, 103 (2016), [arXiv:1507.04546 [hep-th]]. [DOI:10.1007/JHEP02(2016)103]

M. Smolkin and N. Turok, "Dual description of a 4d cosmology", [arXiv:1211.1322 [hep-th]].

J. L. F. Barbon and E. Rabinovici, "Holography of AdS vacuum bubbles", JHEP 1004, 123 (2010), [arXiv:1003.4966 [hep-th]]. [DOI:10.1007/JHEP04(2010)123]

J. Garriga, "Holographic description of vacuum bubbles", Prog. Theor. Phys. Suppl. 190, 261 (2011), [arXiv:1012.5996 [hep-th]]. [DOI:10.1143/PTPS.190.261]

J. Maldacena, "Vacuum decay into Anti de Sitter space", [arXiv:1012.0274 [hep-th]].

S. P. Kumar and V. Vaganov, "Probing crunching AdS cosmologies", JHEP 1602, 026 (2016), [arXiv:1510.03281 [hep-th]]. [DOI:10.1007/JHEP02(2016)026]

H. Ooguri and C. Vafa, "Non-supersymmetric AdS and the Swampland", Adv. Theor. Math. Phys. 21, 1787 (2017), [arXiv:1610.01533 [hep-th]]. [DOI:10.4310/ATMP.2017.v21.n7.a8]

W. Lee, B.-H. Lee, Ch. H. Lee and Ch. Park, "False vacuum bubble nucleation due to a nonminimally coupled scalar field", Phys. Rev. D 74, 123520 (2006), [arXiv:hep-th/0604064]. [DOI:10.1103/PhysRevD.74.123520]