Abstract
The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional \( \mathcal{N} \) = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of a new \( \mathcal{N} \) = 1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3) × ℤ2-invariant truncation of the \( \mathcal{N} \) = 8 theory to an \( \mathcal{N} \) = 1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the \( \mathcal{N} \) = 1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3) × ℤ2-invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional \( {\mathbb{Z}}_2^3 \)-invariant scalar manifold (SU(1, 1)/U(1))7, for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new \( \mathcal{N} \) = 1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an \( \mathcal{N} \) = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I.M. Comsa, M. Firsching and T. Fischbacher, SO(8) Supergravity and the magic of machine learning, JHEP08 (2019) 057 [arXiv:1906.00207] [INSPIRE].
B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys.B 208 (1982) 323 [INSPIRE].
N.P. Warner, Some properties of the scalar potential in gauged supergravity theories, Nucl. Phys.B 231 (1984) 250 [INSPIRE].
N.P. Warner, Some new extrema of the scalar potential of gauged N = 8 supergravity, Phys. Lett.B 128 (1983) 169 [INSPIRE].
B. de Wit, H. Nicolai and N.P. Warner, The embedding of gauged N = 8 supergravity into d = 11 supergravity, Nucl. Phys.B 255 (1985) 29 [INSPIRE].
B. de Wit and H. Nicolai, The consistency of the S7truncation in D = 11 supergravity, Nucl. Phys.B 281 (1987) 211 [INSPIRE].
H. Nicolai and K. Pilch, Consistent truncation of d = 11 supergravity on AdS4× S7 , JHEP03 (2012) 099 [arXiv:1112.6131] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev.D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].
A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys.B 811 (2009) 66 [arXiv:0709.1260] [INSPIRE].
M. Benna, I. Klebanov, T. Klose and M. Smedback, Superconformal Chern-Simons theories and AdS4/CFT3correspondence, JHEP09 (2008) 072 [arXiv:0806.1519] [INSPIRE].
I. Klebanov, T. Klose and A. Murugan, AdS4/CFT3squashed, stretched and warped, JHEP03 (2009) 140 [arXiv:0809.3773] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, JHEP06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
T. Fischbacher, K. Pilch and N.P. Warner, New supersymmetric and stable, non-supersymmetric phases in supergravity and holographic field theory, arXiv:1010.4910 [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys.21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].
T. Fischbacher, The many vacua of gauged extended supergravities, Gen. Rel. Grav.41 (2009) 315 [arXiv:0811.1915] [INSPIRE].
T. Fischbacher, Mapping the vacuum structure of gauged maximal supergravities: an application of high performance symbolic algebra, Ph.D. thesis, Max Planck Inst., Potsdam, Germany (2003) [hep-th/0305176] [INSPIRE].
T. Fischbacher, Fourteen new stationary points in the scalar potential of SO(8)-gauged N = 8, D = 4 supergravity, JHEP09 (2010) 068 [arXiv:0912.1636] [INSPIRE].
T. Fischbacher, Numerical tools to validate stationary points of SO(8)-gauged N = 8 D = 4 supergravity, Comput. Phys. Commun.183 (2012) 780 [arXiv:1007.0600] [INSPIRE].
T. Fischbacher, The encyclopedic reference of critical points for SO(8)-gauged N = 8 supergravity. Part 1: cosmological constants in the range −Λ/g2 ∈ [6 : 14.7), arXiv:1109.1424 [INSPIRE].
M. Trigiante, Gauged supergravities, Phys. Rept.680 (2017) 1 [arXiv:1609.09745] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Charting the landscape of N = 4 flux compactifications, JHEP03 (2011) 137 [arXiv:1102.0239] [INSPIRE].
G. Dall’Agata and G. Inverso, On the vacua of N = 8 gauged supergravity in 4 dimensions, Nucl. Phys.B 859 (2012) 70 [arXiv:1112.3345] [INSPIRE].
G. Inverso, Fluxes and non-perturbative effects in string and M/F theory and their supergravity description, Ph.D. thesis, Rome U., Rome, Italy, 29 October 2013.
A. Borghese, A. Guarino and D. Roest, Triality, periodicity and stability of SO(8) gauged supergravity, JHEP05 (2013) 107 [arXiv:1302.6057] [INSPIRE].
A. Borghese, A. Guarino and D. Roest, All G2invariant critical points of maximal supergravity, JHEP12 (2012) 108 [arXiv:1209.3003] [INSPIRE].
A. Borghese, G. Dibitetto, A. Guarino, D. Roest and O. Varela, The SU(3)-invariant sector of new maximal supergravity, JHEP03 (2013) 082 [arXiv:1211.5335] [INSPIRE].
G. Dall’Agata, G. Inverso and M. Trigiante, Evidence for a family of SO(8) gauged supergravity theories, Phys. Rev. Lett.109 (2012) 201301 [arXiv:1209.0760] [INSPIRE].
A. Gallerati, H. Samtleben and M. Trigiante, The N > 2 supersymmetric AdS vacua in maximal supergravity, JHEP12 (2014) 174 [arXiv:1410.0711] [INSPIRE].
M. Abadi et al., TensorFlow: a system for large-scale machine learning, in 12thUSENIX symposium on operating systems design and implementation (OSDI 16), (2016), pg. 265.
S. Ferrara and S. Sabharwal, Quaternionic manifolds for type II superstring vacua of Calabi-Yau spaces, Nucl. Phys.B 332 (1990) 317 [INSPIRE].
M. Bodner and A.C. Cadavid, Dimensional reduction of type IIB supergravity and exceptional quaternionic manifolds, Class. Quant. Grav.7 (1990) 829 [INSPIRE].
K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, Adv. Theor. Math. Phys.4 (2002) 627 [hep-th/0006066] [INSPIRE].
E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys.B 159 (1979) 141 [INSPIRE].
N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Supergravity instabilities of non-supersymmetric quantum critical points, Class. Quant. Grav.27 (2010) 235013 [arXiv:1006.2546] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge Univ. Press, Cambridge, U.K. (2012).
Wolfram Research Inc., Mathematica, version 11.3, Champaign, IL, U.S.A. (2019).
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys.144 (1982) 249 [INSPIRE].
B. de Wit and H. Nicolai, A new SO(7) invariant solution of d = 11 supergravity, Phys. Lett.B 148 (1984) 60 [INSPIRE].
B. Biran, F. Englert, B. de Wit and H. Nicolai, Gauged N = 8 supergravity and its breaking from spontaneous compactification, Phys. Lett.B 124 (1983) 45 [Erratum ibid.B 128 (1983) 461] [INSPIRE].
B. de Wit and H. Nicolai, The parallelizing S7torsion in gauged N = 8 supergravity, Nucl. Phys.B 231 (1984) 506 [INSPIRE].
N. Bobev, K. Pilch and N.P. Warner, Supersymmetric Janus solutions in four dimensions, JHEP06 (2014) 058 [arXiv:1311.4883] [INSPIRE].
D.R. Grayson and M.E. Stillman, Macaulay2, a software system for research in algebraic geometry, https://faculty.math.illinois.edu/Macaulay2/.
D.J. Bates, J.D. Hauenstein, A.J. Sommese and C.W. Wampler, Bertini: a software package for numerical algebraic geometry, Bertini home page, (2013).
J.D. Hauenstein and C.W. Wampler, Unification and extension of intersection algorithms in numerical algebraic geometry, Appl. Math. Comput.293 (2017) 226.
N. Bobev, V.S. Min and K. Pilch, Mass-deformed ABJM and black holes in AdS4, JHEP03 (2018) 050 [arXiv:1801.03135] [INSPIRE].
C.-H. Ahn and K. Woo, Supersymmetric domain wall and RG flow from 4-dimensional gauged N = 8 supergravity, Nucl. Phys.B 599 (2001) 83 [hep-th/0011121] [INSPIRE].
C.-H. Ahn and T. Itoh, An N = 1 supersymmetric G2invariant flow in M-theory, Nucl. Phys.B 627 (2002) 45 [hep-th/0112010] [INSPIRE].
C.-H. Ahn and K.-S. Woo, Domain wall and membrane flow from other gauged d = 4, N = 8 supergravity. Part 1, Nucl. Phys.B 634 (2002) 141 [hep-th/0109010] [INSPIRE].
C.-H. Ahn and K.-S. Woo, Domain wall from gauged d = 4, N = 8 supergravity. Part 2, JHEP11 (2003) 014 [hep-th/0209128] [INSPIRE].
N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Holographic, N = 1 supersymmetric RG flows on M2 branes, JHEP09 (2009) 043 [arXiv:0901.2736] [INSPIRE].
D.Z. Freedman and S.S. Pufu, The holography of F-maximization, JHEP03 (2014) 135 [arXiv:1302.7310] [INSPIRE].
M.J. Duff and S. Ferrara, E7and the tripartite entanglement of seven qubits, Phys. Rev.D 76 (2007) 025018 [quant-ph/0609227] [INSPIRE].
L. Borsten, M.J. Duff and P. Levay, The black-hole/qubit correspondence: an up-to-date review, Class. Quant. Grav.29 (2012) 224008 [arXiv:1206.3166] [INSPIRE].
M.J. Duff and S. Ferrara, Four curious supergravities, Phys. Rev.D 83 (2011) 046007 [arXiv:1010.3173] [INSPIRE].
S. Ferrara and R. Kallosh, Seven-disk manifold, α-attractors and B modes, Phys. Rev.D 94 (2016) 126015 [arXiv:1610.04163] [INSPIRE].
J.C. Baez, The octonions, Bull. Am. Math. Soc.39 (2002) 145 [Erratum ibid.42 (2005) 213] [math.RA/0105155] [INSPIRE].
R.W. Hamming, Error detecting and error correcting codes, Bell Syst. Tech. J.29 (1950) 147.
T. Fischbacher, Binary error correcting codes and maximal supergravity, work in progress.
N. Bobev, T. Fischbacher and K. Pilch, Holography and the seven-disk manifold, in progress.
S. Gukov, Counting RG flows, JHEP01 (2016) 020 [arXiv:1503.01474] [INSPIRE].
G. Dall’Agata, G. Inverso and A. Marrani, Symplectic deformations of gauged maximal supergravity, JHEP07 (2014) 133 [arXiv:1405.2437] [INSPIRE].
A. Guarino and O. Varela, Dyonic ISO(7) supergravity and the duality hierarchy, JHEP02 (2016) 079 [arXiv:1508.04432] [INSPIRE].
N. Bobev, T. Fischbacher, F. Gautason and K. Pilch, Searching for vacua of SO(6)-gauged maximal five-dimensional supergravity, in progress.
N. Yamatsu, Finite-dimensional Lie algebras and their representations for unified model building, arXiv:1511.08771 [INSPIRE].
E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in Strings, Branes and Extra Dimensions: TASI 2001: Proceedings, (2002), pg. 3 [hep-th/0201253] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of superconformal symmetry in diverse dimensions, JHEP03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys.B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett.B 431 (1998) 63 [hep-th/9803251] [INSPIRE].
W.S. l’Yi, Correlators of currents corresponding to the massive p form fields in AdS/CFT correspondence, Phys. Lett.B 448 (1999) 218 [hep-th/9811097] [INSPIRE].
A. Volovich, Rarita-Schwinger field in the AdS/CFT correspondence, JHEP09 (1998) 022 [hep-th/9809009] [INSPIRE].
S. Corley, The massless gravitino and the AdS/CFT correspondence, Phys. Rev.D 59 (1999) 086003 [hep-th/9808184] [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: 1909.10969
Electronic supplementary material
ESM 1
(ZIP 182 kb)
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Bobev, N., Fischbacher, T. & Pilch, K. Properties of the new \( \mathcal{N} \) = 1 AdS4 vacuum of maximal supergravity. J. High Energ. Phys. 2020, 99 (2020). https://doi.org/10.1007/JHEP01(2020)099
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2020)099