Abstract
We describe a one-parameter family of new holographic RG flows that start from AdS 4 × S 7 and go to \( \widehat{Ad{S}_5}\times \mathrm{\mathcal{B}}6 \), where \( \mathrm{\mathcal{B}}6 \) is conformal to a Kähler manifold and \( \widehat{Ad{S}_5} \) is Poincaré AdS 5 with one spatial direction compactified and fibered over \( \mathrm{\mathcal{B}}6 \). The new solutions “flow up dimensions,” going from the (2 + 1)-dimensional conformal field theory on M2 branes in the UV to a (3 + 1)-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincaré sections of the \( \widehat{Ad{S}_5} \) are the (3 + 1)-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional \( \mathcal{N}=2 \) supersymmetric flow in \( \mathcal{N}=8 \) gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. The eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
I. Bena, N. Bobev, C. Ruef and N.P. Warner, Supertubes in Bubbling Backgrounds: Born-Infeld Meets Supergravity, JHEP 07 (2009) 106 [arXiv:0812.2942] [INSPIRE].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].
P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [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 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 T. Itoh, An N = 1 supersymmetric G-2 invariant flow in M-theory, Nucl. Phys. B 627 (2002) 45 [hep-th/0112010] [INSPIRE].
C.-h. Ahn and T. Itoh, The eleven-dimensional metric for AdS/CFT RG flows with common SU(3) invariance, Nucl. Phys. B 646 (2002) 257 [hep-th/0208137] [INSPIRE].
C.-h. Ahn and K.-s. Woo, Domain wall from gauged D = 4, N = 8 supergravity. Part 2, JHEP 11 (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, JHEP 09 (2009) 043 [arXiv:0901.2736] [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].
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].
R. Corrado, K. Pilch and N.P. Warner, An N = 2 supersymmetric membrane flow, Nucl. Phys. B 629 (2002) 74 [hep-th/0107220] [INSPIRE].
M. Benna, I. Klebanov, T. Klose and M. Smedback, Superconformal Chern-Simons Theories and AdS 4 /CFT 3 Correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [INSPIRE].
M. Cvetič, S.S. Gubser, H. Lü and C.N. Pope, Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories, Phys. Rev. D 62 (2000) 086003 [hep-th/9909121] [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Consistent sphere reductions and universality of the Coulomb branch in the domain wall/QFT correspondence, Nucl. Phys. B 590 (2000) 213 [hep-th/0004201] [INSPIRE].
C.N. Gowdigere and N.P. Warner, Flowing with eight supersymmetries in M-theory and F-theory, JHEP 12 (2003) 048 [hep-th/0212190] [INSPIRE].
P. Kraus, F. Larsen and S.P. Trivedi, The Coulomb branch of gauge theory from rotating branes, JHEP 03 (1999) 003 [hep-th/9811120] [INSPIRE].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Continuous distributions of D3-branes and gauged supergravity, JHEP 07 (2000) 038 [hep-th/9906194] [INSPIRE].
C.N. Gowdigere and N.P. Warner, Holographic Coulomb branch flows with N = 1 supersymmetry, JHEP 03 (2006) 049 [hep-th/0505019] [INSPIRE].
C.N. Pope and N.P. Warner, A dielectric flow solution with maximal supersymmetry, JHEP 04 (2004) 011 [hep-th/0304132] [INSPIRE].
I. Bena and N.P. Warner, A Harmonic family of dielectric flow solutions with maximal supersymmetry, JHEP 12 (2004) 021 [hep-th/0406145] [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
N. Bobev, K. Pilch and N.P. Warner, Supersymmetric Janus Solutions in Four Dimensions, JHEP 06 (2014) 058 [arXiv:1311.4883] [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, d = 11 Supergravity With Local SU(8) Invariance, Nucl. Phys. B 274 (1986) 363 [INSPIRE].
B. de Wit and H. Nicolai, The Consistency of the S 7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].
H. Nicolai and K. Pilch, Consistent Truncation of D = 11 Supergravity on AdS 4 × S 7, JHEP 03 (2012) 099 [arXiv:1112.6131] [INSPIRE].
B. de Wit and H. Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions, JHEP 05 (2013) 077 [arXiv:1302.6219] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Testing the non-linear flux ansatz for maximal supergravity, Phys. Rev. D 87 (2013) 085038 [arXiv:1303.1013] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Nonlinear Kaluza-Klein theory for dual fields, Phys. Rev. D 88 (2013) 125002 [arXiv:1309.0266] [INSPIRE].
K. Pilch, A. Tyukov and N.P. Warner, to appear.
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [INSPIRE].
O.J. Ganor and A. Hanany, Small E 8 instantons and tensionless noncritical strings, Nucl. Phys. B 474 (1996) 122 [hep-th/9602120] [INSPIRE].
N. Seiberg and E. Witten, Comments on string dynamics in six-dimensions, Nucl. Phys. B 471 (1996) 121 [hep-th/9603003] [INSPIRE].
M.J. Duff, H. Lü and C.N. Pope, Heterotic phase transitions and singularities of the gauge dyonic string, Phys. Lett. B 378 (1996) 101 [hep-th/9603037] [INSPIRE].
E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys. B 471 (1996) 195 [hep-th/9603150] [INSPIRE].
A. Klemm, W. Lerche, P. Mayr, C. Vafa and N.P. Warner, Selfdual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746 [hep-th/9604034] [INSPIRE].
O.J. Ganor, Six-dimensional tensionless strings in the large-N limit, Nucl. Phys. B 489 (1997) 95 [hep-th/9605201] [INSPIRE].
C. Hoyos, Higher dimensional conformal field theories in the Coulomb branch, Phys. Lett. B 696 (2011) 145 [arXiv:1010.4438] [INSPIRE].
D. Young and K. Zarembo, Holographic Dual of the Eguchi-Kawai Mechanism, JHEP 06 (2014) 030 [arXiv:1404.0225] [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].
D.N. Page and C.N. Pope, Inhomogeneous Einstein Metrics On Complex Line Bundles, Class. Quant. Grav. 4 (1987) 213 [INSPIRE].
J.P. Gauntlett, D. Martelli, J.F. Sparks and D. Waldram, A new infinite class of Sasaki-Einstein manifolds, Adv. Theor. Math. Phys. 8 (2006) 987 [hep-th/0403038] [INSPIRE].
C.N. Gowdigere, D. Nemeschansky and N.P. Warner, Supersymmetric solutions with fluxes from algebraic Killing spinors, Adv. Theor. Math. Phys. 7 (2004) 787 [hep-th/0306097] [INSPIRE].
K. Pilch and N.P. Warner, N = 1 supersymmetric solutions of IIB supergravity from Killing spinors, hep-th/0403005 [INSPIRE].
D. Nemeschansky and N.P. Warner, A family of M-theory flows with four supersymmetries, hep-th/0403006 [INSPIRE].
N.P. Warner, Holographic renormalization group flows: the view from ten-dimensions, Class. Quant. Grav. 18 (2001) 3159 [hep-th/0011207] [INSPIRE].
D.Z. Freedman and S.S. Pufu, The holography of F -maximization, JHEP 03 (2014) 135 [arXiv:1302.7310] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of M-theory, Class. Quant. Grav. 21 (2004) 4335 [hep-th/0402153] [INSPIRE].
I. Bena, S.F. Ross and N.P. Warner, On the Oscillation of Species, JHEP 09 (2014) 113 [arXiv:1312.3635] [INSPIRE].
S.S. Gubser, Curvature singularities: The good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [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: 1506.01045
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
Pilch, K., Tyukov, A. & Warner, N.P. Flowing to higher dimensions: a new strongly-coupled phase on M2 branes. J. High Energ. Phys. 2015, 170 (2015). https://doi.org/10.1007/JHEP11(2015)170
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)170