Abstract
We present maximal supergravity in two dimensions with gauge group SO(9). The construction is based on selecting the proper embedding of the gauge group into the infinite-dimensional symmetry group of the ungauged theory. The bosonic part of the Lagrangian is given by a (dilaton-)gravity coupled non-linear gauged σ-model with Wess-Zumino term. We give explicit expressions for the fermionic sector, the Yukawa couplings and the scalar potential which supports a half-supersymmetric domain wall solution. The theory is expected to describe the low-energy effective action upon reduction on the D0-brane near-horizon warped AdS 2 ×S 8 geometry, dual to the supersymmetric (BFSS) matrix quantum mechanics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
A. Hashimoto and N. Itzhaki, A Comment on the Zamolodchikov c function and the black string entropy, Phys. Lett. B 454 (1999) 235 [hep-th/9903067] [INSPIRE].
Y. Sekino and T. Yoneya, Generalized AdS/CFT correspondence for matrix theory in the large-N limit, Nucl. Phys. B 570 (2000) 174 [hep-th/9907029] [INSPIRE].
Y. Sekino, Supercurrents in matrix theory and the generalized AdS/CFT correspondence, Nucl. Phys. B 602 (2001) 147 [hep-th/0011122] [INSPIRE].
J. Hiller, O. Lunin, S. Pinsky and U. Trittmann, Towards a SDLCQ test of the Maldacena conjecture, Phys. Lett. B 482 (2000) 409 [hep-th/0003249] [INSPIRE].
T. Gherghetta and Y. Oz, Supergravity, nonconformal field theories and brane worlds, Phys. Rev. D 65 (2002) 046001 [hep-th/0106255] [INSPIRE].
J.F. Morales and H. Samtleben, Supergravity duals of matrix string theory, JHEP 08 (2002) 042 [hep-th/0206247] [INSPIRE].
M. Asano and Y. Sekino, Large-N limit of SYM theories with 16 supercharges from superstrings on Dp-brane backgrounds, Nucl. Phys. B 705 (2005) 33 [hep-th/0405203] [INSPIRE].
J.R. Hiller, S.S. Pinsky, N. Salwen and U. Trittmann, Direct evidence for the Maldacena conjecture for \( \mathcal{N} \) = (8, 8) super Yang-Mills theory in 1+1 dimensions, Phys. Lett. B 624 (2005)105 [hep-th/0506225] [INSPIRE].
T. Wiseman and B. Withers, Holographic renormalization for coincident Dp-branes, JHEP 10 (2008)037 [arXiv:0807.0755] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].
K.N. Anagnostopoulos, M. Hanada, J. Nishimura and S. Takeuchi, Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature, Phys. Rev. Lett. 100 (2008) 021601 [arXiv:0707.4454] [INSPIRE].
S. Catterall and T. Wiseman, Black hole thermodynamics from simulations of lattice Yang-Mills theory, Phys. Rev. D 78 (2008) 041502 [arXiv:0803.4273] [INSPIRE].
S. Catterall, A. Joseph and T. Wiseman, Thermal phases of D1-branes on a circle from lattice super Yang-Mills, JHEP 12 (2010) 022 [arXiv:1008.4964] [INSPIRE].
M. Hanada, J. Nishimura, Y. Sekino and T. Yoneya, Direct test of the gauge-gravity correspondence for Matrix theory correlation functions, JHEP 12 (2011) 020 [arXiv:1108.5153] [INSPIRE].
B. de Wit, J. Hoppe and H. Nicolai, On the Quantum Mechanics of Supermembranes, Nucl. Phys. B 305 (1988) 545 [INSPIRE].
T. Banks, W. Fischler, S. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
H. Boonstra, K. Skenderis and P. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
K. Behrndt, E. Bergshoeff, R. Halbersma and J.P. van der Schaar, On domain wall/QFT dualities in various dimensions, Class. Quant. Grav. 16 (1999) 3517 [hep-th/9907006] [INSPIRE].
E. Bergshoeff, M. Nielsen and D. Roest, The Domain walls of gauged maximal supergravities and their M-theory origin, JHEP 07 (2004) 006 [hep-th/0404100] [INSPIRE].
H. Nicolai, The integrability of N = 16 supergravity, Phys. Lett. B 194 (1987) 402 [INSPIRE].
H. Nicolai and N. Warner, The structure of N = 16 supergravity in two dimensions, Commun. Math. Phys. 125 (1989) 369.
B. Julia, Kac-Moody symmetry of gravitation and supergravity theories, in Lectures in Applied Mathematics AMS-SIAM 21 (1985) 335.
H. Samtleben and M. Weidner, Gauging hidden symmetries in two dimensions, JHEP 08 (2007)076 [arXiv:0705.2606] [INSPIRE].
R.P. Geroch, A Method for generating solutions of Einstein’s equations, J. Math. Phys. 12 (1971) 918 [INSPIRE].
V. Belinsky and V. Zakharov, Integration of the Einstein Equations by the Inverse Scattering Problem Technique and the Calculation of the Exact Soliton Solutions, Sov. Phys. JETP 48 (1978) 985 [INSPIRE].
D. Maison, Are the stationary, axially symmetric Einstein equations completely integrable?, Phys. Rev. Lett. 41 (1978) 521 [INSPIRE].
B. Julia, Infinite Lie algebras in physics, in Johns Hopkins Workshop on Current Problems in Particle Theory (1981).
D. Korotkin and H. Samtleben, Yangian symmetry in integrable quantum gravity, Nucl. Phys. B 527 (1998) 657 [hep-th/9710210] [INSPIRE].
H. Nicolai and H. Samtleben, Integrability and canonical structure of D = 2, N = 16 supergravity, Nucl. Phys. B 533 (1998) 210 [hep-th/9804152] [INSPIRE].
E. Cremmer, B. Julia, H. Lü and C. Pope, Dualization of dualities. 1., Nucl. Phys. B 523 (1998) 73 [hep-th/9710119] [INSPIRE].
T. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
C. Hull and B.J. Spence, The gauged nonlinear σ-model with Wess-Zumino term, Phys. Lett. B 232 (1989) 204 [INSPIRE].
X.C. de la Ossa and F. Quevedo, Duality symmetries from nonAbelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].
P. Fré’, F. Gargiulo, K. Rulik and M. Trigiante, The General pattern of Kac Moody extensions in supergravity and the issue of cosmic billiards, Nucl. Phys. B 741 (2006) 42 [hep-th/0507249] [INSPIRE].
E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].
H. Nicolai and H. Samtleben, Compact and noncompact gauged maximal supergravities in three-dimensions, JHEP 04 (2001) 022 [hep-th/0103032] [INSPIRE].
N. Marcus and J.H. Schwarz, Three-Dimensional Supergravity Theories, Nucl. Phys. B 228 (1983) 145 [INSPIRE].
V. Kac and M. Sanielevici, Decompositions of representations of exceptional affine algebras with respect to conformal subalgebras, Phys. Rev. D 37 (1988) 2231 [INSPIRE].
E. Bergshoeff, M. de Roo, M.B. Green, G. Papadopoulos and P. Townsend, Duality of type-II 7 branes and 8 branes, Nucl. Phys. B 470 (1996) 113 [hep-th/9601150] [INSPIRE].
H. Nicolai and H. Samtleben, Maximal gauged supergravity in three-dimensions, Phys. Rev. Lett. 86 (2001) 1686 [hep-th/0010076] [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, On Lagrangians and gaugings of maximal supergravities, Nucl. Phys. B 655 (2003) 93 [hep-th/0212239] [INSPIRE].
B. de Wit and H. Samtleben, Gauged maximal supergravities and hierarchies of nonAbelian vector-tensor systems, Fortsch. Phys. 53 (2005) 442 [hep-th/0501243] [INSPIRE].
K. Peeters, A Field-theory motivated approach to symbolic computer algebra, Comput. Phys. Commun. 176 (2007) 550 [cs/0608005] [INSPIRE].
K. Peeters, Introducing Cadabra: A Symbolic computer algebra system for field theory problems, hep-th/0701238 [INSPIRE].
M. Cvetič, H. Lü and C. Pope, Consistent Kaluza-Klein sphere reductions, Phys. Rev. D 62 (2000)064028 [hep-th/0003286] [INSPIRE].
H. Nicolai and H. Samtleben, A U(1) × SO(9) invariant compactification of D = 11 supergravity to two dimensions, in Non-perturbative Quantum Effects 2000, PoS(tmr2000)014.
E.A. Bergshoeff, A. Kleinschmidt and F. Riccioni, Supersymmetric Domain Walls, Phys. Rev. D 86 (2012) 085043 [arXiv:1206.5697] [INSPIRE].
H. Nicolai and H. Samtleben, On K(E9 ), Q. J. Pure Appl. Math. 1 (2005) 180 [hep-th/0407055] [INSPIRE].
L. Paulot, Infinite-Dimensional Gauge Structure of D = 2 N = 16 Supergravity, hep-th/0604098 [INSPIRE].
T. Damour, A. Kleinschmidt and H. Nicolai, K(E 10 ), Supergravity and Fermions, JHEP 08 (2006)046 [hep-th/0606105] [INSPIRE].
D. Youm, (Generalized) conformal quantum mechanics of 0-branes and two-dimensional dilaton gravity, Nucl. Phys. B 573 (2000) 257 [hep-th/9909180] [INSPIRE].
M. Cvetič, H. Lü and C. Pope, Consistent warped space Kaluza-Klein reductions, half maximal gauged supergravities and CP n constructions, Nucl. Phys. B 597 (2001) 172 [hep-th/0007109] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1210.4266
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Ortiz, T., Samtleben, H. SO(9) supergravity in two dimensions. J. High Energ. Phys. 2013, 183 (2013). https://doi.org/10.1007/JHEP01(2013)183
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2013)183