Abstract
Gauged \( \mathcal{N}=8 \) supergravity in four dimensions is now known to admit a deformation characterized by a real parameter ω lying in the interval 0 ≤ ω ≤ π/8. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full \( \mathcal{N}=8 \) supersymmetry can be maintained by the boundary conditions only for ω = 0. For non-vanishing ω, and requiring that there be no propagating spin s > 1 fields on the boundary, we show that \( \mathcal{N}=3 \) is the maximum degree of supersymmetry that can be preserved by the boundary conditions. We then construct in detail the consistent truncation of the \( \mathcal{N}=8 \) theory to give ω-deformed SO(6) gauged \( \mathcal{N}=6 \) supergravity, again with ω in the range 0 ≤ ω ≤ π/8. We show that this theory admits fully \( \mathcal{N}=6 \) supersymmetry-preserving boundary conditions not only for ω = 0, but also for ω = π/8. These two theories are related by a U(1) electric-magnetic duality. We observe that the only three-point functions that depend on ω involve the coupling of an SO(6) gauge field with the U(1) gauge field and a scalar or pseudo-scalar field. We compute these correlation functions and compare them with those of the undeformed \( \mathcal{N}=6 \) theory. We find that the correlation functions in the ω=π/8 theory holographically correspond to amplitudes in the U(N) k ×U(N)−k ABJM model in which the U(1) Noether current is replaced by a dynamical U(1) gauge field. We also show that the ω-deformed \( \mathcal{N}=6 \) gauged supergravities can be obtained via consistent reductions from the eleven-dimensional or ten-dimensional type IIA supergravities.
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References
B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, The maximal D = 4 supergravities, JHEP 06 (2007) 049 [arXiv:0705.2101] [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].
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].
L. Andrianopoli, R. D’Auria, S. Ferrara, P.A. Grassi and M. Trigiante, Exceptional N = 6 and N = 2 AdS 4 supergravity and zero-center modules, JHEP 04 (2009) 074 [arXiv:0810.1214] [INSPIRE].
E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
B. de Wit, Supergravity, hep-th/0212245 [INSPIRE].
H. Lü, Y. Pang and C.N. Pope, An ω deformation of gauged STU supergravity, JHEP 04 (2014) 175 [arXiv:1402.1994] [INSPIRE].
G. Dall’Agata, G. Inverso and A. Marrani, Symplectic deformations of gauged maximal supergravity, JHEP 07 (2014) 133 [arXiv:1405.2437] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
A. Ishibashi and R.M. Wald, Dynamics in nonglobally hyperbolic static space-times. 3. Anti-de Sitter space-time, Class. Quant. Grav. 21 (2004) 2981 [hep-th/0402184] [INSPIRE].
D. Marolf and S.F. Ross, Boundary conditions and new dualities: vector fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].
G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [INSPIRE].
A.J. Amsel and G. Compere, Supergravity at the boundary of AdS supergravity, Phys. Rev. D 79 (2009) 085006 [arXiv:0901.3609] [INSPIRE].
S. Hollands and D. Marolf, Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry, Class. Quant. Grav. 24 (2007) 2301 [gr-qc/0611044] [INSPIRE].
A.J. Amsel and D. Marolf, Supersymmetric multi-trace boundary conditions in AdS, Class. Quant. Grav. 26 (2009) 025010 [arXiv:0808.2184] [INSPIRE].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton and gauge boson propagators in AdS d+1, Nucl. Phys. B 562 (1999) 330 [hep-th/9902042] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT d /AdS d+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
S.W. Hawking, The boundary conditions for gauged supergravity, Phys. Lett. B 126 (1983) 175 [INSPIRE].
S. Giombi, S. Prakash and X. Yin, A note on CFT correlators in three dimensions, JHEP 07 (2013) 105 [arXiv:1104.4317] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M 2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
A. Gallerati, H. Samtleben and M. Trigiante, The N > 2 supersymmetric AdS vacua in maximal supergravity, JHEP 12 (2014) 174 [arXiv:1410.0711] [INSPIRE].
C.N. Pope, Consistency of truncations in Kaluza-Klein, Conf. Proc. C 841031 (1984) 429 [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].
B.E.W. Nilsson and C.N. Pope, Hopf fibration of eleven-dimensional supergravity, Class. Quant. Grav. 1 (1984) 499 [INSPIRE].
H. Lü, C.N. Pope and P.K. Townsend, Domain walls from anti-de Sitter space-time, Phys. Lett. B 391 (1997) 39 [hep-th/9607164] [INSPIRE].
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ArXiv ePrint: 1411.6020
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Borghese, A., Pang, Y., Pope, C.N. et al. Correlation functions in ω-deformed \( \mathcal{N}=6 \) supergravity. J. High Energ. Phys. 2015, 112 (2015). https://doi.org/10.1007/JHEP02(2015)112
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DOI: https://doi.org/10.1007/JHEP02(2015)112