Abstract
In this paper we discuss some special (critical) background solutions that arise in topological gauged \( \mathcal{N} \) = 8 three-dimensional CFTs with SO(N) gauge group. Depending on how many scalar fields are given a VEV the theory has background solutions for certain values of μl, where μ and l are parameters in the TMG Lagrangian. Apart from Minkowski, chiral round AdS 3 and null-warped AdS 3 (or Schrödinger(z = 2)) we identify also a more exotic solution recently found in TMG by Ertl, Grumiller and Johansson. We also discuss the spectrum, symmetry breaking pattern and the supermultiplet structure in the various backgrounds and argue that some properties are due to their common origin in a conformal phase. Some of the scalar fields, including all higgsed ones, turn out to satisfy three-dimensional field equations similar to those of the singleton. Finally, we note that topologically gauged \( \mathcal{N} \) = 6 ABJ(M) theories have a similar, but more restricted, set of background solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
U. Gran and B.E.W. Nilsson, Three-dimensional N = 8 superconformal gravity and its coupling to BLG M2-branes, JHEP 03 (2009) 074 [arXiv:0809.4478] [INSPIRE].
U. Gran, J. Greitz, P.S. Howe and B.E.W. Nilsson, Topologically gauged superconformal Chern-Simons matter theories, JHEP 12 (2012) 046 [arXiv:1204.2521] [INSPIRE].
P. van Nieuwenhuizen, D = 3 Conformal Supergravity and Chern-Simons Terms, Phys. Rev. D 32 (1985) 872 [INSPIRE].
U. Lindström and M. Roček, Superconformal Gravity in Three-dimensions as a Gauge Theory, Phys. Rev. Lett. 62 (1989) 2905 [INSPIRE].
J. Bagger and N. Lambert, Modeling Multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [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].
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].
X. Chu and B.E.W. Nilsson, Three-dimensional topologically gauged N = 6 ABJM type theories, JHEP 06 (2010) 057 [arXiv:0906.1655] [INSPIRE].
P.S. Howe, J.M. Izquierdo, G. Papadopoulos and P.K. Townsend, New supergravities with central charges and Killing spinors in (2 + 1)-dimensions, Nucl. Phys. B 467 (1996) 183 [hep-th/9505032] [INSPIRE].
M. Cederwall, U. Gran and B.E.W. Nilsson, D = 3, N = 8 conformal supergravity and the Dragon window, JHEP 09 (2011) 101 [arXiv:1103.4530] [INSPIRE].
X. Chu, H. Nastase, B.E.W. Nilsson and C. Papageorgakis, Higgsing M2 to D2 with gravity: N =6 chiral supergravity from topologically gauged ABJM theory, JHEP 04 (2011) 040 [arXiv:1012.5969] [INSPIRE].
W. Li, W. Song and A. Strominger, Chiral Gravity in Three Dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].
A. Maloney, W. Song and A. Strominger, Chiral Gravity, Log Gravity and Extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [INSPIRE].
S. Deser and J.H. Kay, Topologically massive supergravity, Phys. Lett. B 120 (1983) 97 [INSPIRE].
M. Becker, P. Bruillard and S. Downes, Chiral Supergravity, JHEP 10 (2009) 004 [arXiv:0906.4822] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, arXiv:1108.5735 [INSPIRE].
A. Bagchi and R. Gopakumar, Galilean Conformal Algebras and AdS/CFT, JHEP 07 (2009) 037 [arXiv:0902.1385] [INSPIRE].
A. Bagchi, S. Detournay and D. Grumiller, Flat-Space Chiral Gravity, Phys. Rev. Lett. 109 (2012) 151301 [arXiv:1208.1658] [INSPIRE].
D.T. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].
A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [INSPIRE].
D. Grumiller, W. Riedler, J. Rosseel and T. Zojer, Holographic applications of logarithmic conformal field theories, J. Phys. A 46 (2013) 494002 [arXiv:1302.0280] [INSPIRE].
D. Anninos, G. Compere, S. de Buyl, S. Detournay and M. Guica, The Curious Case of Null Warped Space, JHEP 11 (2010) 119 [arXiv:1005.4072] [INSPIRE].
E.A. Bergshoeff, S. de Haan, W. Merbis, M. Porrati and J. Rosseel, Unitary Truncations and Critical Gravity: a Toy Model, JHEP 04 (2012) 134 [arXiv:1201.0449] [INSPIRE].
A. Strominger, A Simple Proof of the Chiral Gravity Conjecture, arXiv:0808.0506 [INSPIRE].
D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 Black Holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].
S. Ertl, D. Grumiller and N. Johansson, All stationary axi-symmetric local solutions of topologically massive gravity, Class. Quant. Grav. 27 (2010) 225021 [arXiv:1006.3309] [INSPIRE].
H.R. Afshar, M. Alishahiha and A.E. Mosaffa, Quasi-Normal Modes of Extremal BTZ Black Holes in TMG, JHEP 08 (2010) 081 [arXiv:1006.4468] [INSPIRE].
S. Deser and J. Franklin, Is BTZ a separate superselection sector of CTMG?, Phys. Lett. B 693 (2010) 609 [arXiv:1007.2637] [INSPIRE].
G.W. Gibbons, C.N. Pope and E. Sezgin, The General Supersymmetric Solution of Topologically Massive Supergravity, Class. Quant. Grav. 25 (2008) 205005 [arXiv:0807.2613] [INSPIRE].
D.D.K. Chow, C.N. Pope and E. Sezgin, Classification of solutions in topologically massive gravity, Class. Quant. Grav. 27 (2010) 105001 [arXiv:0906.3559] [INSPIRE].
D.D.K. Chow, C.N. Pope and E. Sezgin, Kundt spacetimes as solutions of topologically massive gravity, Class. Quant. Grav. 27 (2010) 105002 [arXiv:0912.3438] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
K. Siampos and P. Spindel, Solutions of massive gravity theories in constant scalar invariant geometries, Class. Quant. Grav. 30 (2013) 145014 [arXiv:1302.6250] [INSPIRE].
G. Clement, Particle - like solutions to topologically massive gravity, Class. Quant. Grav. 11 (1994) L115 [gr-qc/9404004] [INSPIRE].
M. Blau, J. Hartong and B. Rollier, Geometry of Schrödinger Space-Times, Global Coordinates and Harmonic Trapping, JHEP 07 (2009) 027 [arXiv:0904.3304] [INSPIRE].
G. Compere, S. de Buyl and S. Detournay, Non-Einstein geometries in Chiral Gravity, JHEP 10 (2010) 042 [arXiv:1006.3099] [INSPIRE].
M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991] [INSPIRE].
P. Kraus and E. Perlmutter, Universality and exactness of Schrödinger geometries in string and M-theory, JHEP 05 (2011) 045 [arXiv:1102.1727] [INSPIRE].
J. Wang, Schrödinger Fermi Liquids, Phys. Rev. D 89 (2014) 046008 [arXiv:1301.1986] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. Gonzalez, The Flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].
S. Mukhi and C. Papageorgakis, M2 to D2, JHEP 05 (2008) 085 [arXiv:0803.3218] [INSPIRE].
S. Mukhi, Unravelling the novel Higgs mechanism in (2 + 1)d Chern-Simons theories, JHEP 12 (2011) 083 [arXiv:1110.3048] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
P.K. Townsend, K. Pilch and P. van Nieuwenhuizen, Selfduality in Odd Dimensions, Phys. Lett. B 136 (1984) 38 [Addendum ibid. B 137 (1984) 443] [INSPIRE].
S. Moroz, Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence, Phys. Rev. D 81 (2010) 066002 [arXiv:0911.4060] [INSPIRE].
X. Bekaert, E. Meunier and S. Moroz, Towards a gravity dual of the unitary Fermi gas, Phys. Rev. D 85 (2012) 106001 [arXiv:1111.1082] [INSPIRE].
M. Flato and C. Fronsdal, Three-dimensional singletons, Lett. Math. Phys. 20 (1990) 65 [INSPIRE].
B.E.W. Nilsson, Light-cone analysis of ungauged and topologically gauged BLG theories, Class. Quant. Grav. 26 (2009) 175001 [arXiv:0811.3388] [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].
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].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W-symmetry in AdS 3, JHEP 02 (2011) 004 [arXiv:1009.6087] [INSPIRE].
B.E.W. Nilsson, Aspects of topologically gauged M2-branes with six supersymmetries: towards a ‘sequential AdS/CFT’?, arXiv:1203.5090 [INSPIRE].
M.A. Vasiliev, Conformal higher spin symmetries of 4 − D massless supermultiplets and osp(L,2 M) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006 [hep-th/0106149] [INSPIRE].
M.A. Vasiliev, Holography, Unfolding and Higher-Spin Theory, J. Phys. A 46 (2013) 214013 [arXiv:1203.5554] [INSPIRE].
G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [INSPIRE].
O. Aharony, D. Marolf and M. Rangamani, Conformal field theories in anti-de Sitter space, JHEP 02 (2011) 041 [arXiv:1011.6144] [INSPIRE].
M. Berg and H. Samtleben, An Exact holographic RG flow between 2 − D conformal fixed points, JHEP 05 (2002) 006 [hep-th/0112154] [INSPIRE].
C. Cunliff, Non-Fefferman-Graham asymptotics and holographic renormalization in New Massive Gravity, JHEP 04 (2013) 141 [arXiv:1301.1347] [INSPIRE].
H. Ahmedov and A.N. Aliev, Exact Solutions in D-3 New Massive Gravity, Phys. Rev. Lett. 106 (2011) 021301 [arXiv:1006.4264] [INSPIRE].
H. Ahmedov and A.N. Aliev, The General Type N Solution of New Massive Gravity, Phys. Lett. B 694 (2010) 143 [arXiv:1008.0303] [INSPIRE].
N.S. Deger, A. Kaya, H. Samtleben and E. Sezgin, Supersymmetric Warped AdS in Extended Topologically Massive Supergravity, arXiv:1311.4583 [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: 1304.2270
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
Nilsson, B.E.W. Critical solutions of topologically gauged \( \mathcal{N} \) = 8 CFTs in three dimensions. J. High Energ. Phys. 2014, 107 (2014). https://doi.org/10.1007/JHEP04(2014)107
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)107