Abstract
We consider Einstein gravity coupled to an n-form field strength in D dimensions. Such a theory cannot be supersymmetrized in general, we nevertheless propose a pseudo-Killing spinor equation and show that the AdS × Sphere vacua have the maximum number of pseudo-Killing spinors, and hence are fully pseudo-supersymmetric. We show that extremal p-branes and their intersecting configurations preserve fractions of the pseudo-supersymmetry. We study the integrability condition for general (D, n) and obtain the additional constraints that are required so that the existence of the pseudo-Killing spinors implies the Einstein equations of motion. We obtain new pseudo-supersymmetric bubbling AdS5 × S 5 spaces that are supported by a non-self-dual 5-form. This demonstrates that non-supersymmegtric conformal field theories may also have bubbling states of arbitrary droplets of free fermions in the phase space. We also obtain an example of less-bubbling AdS geometry in D = 8, whose bubbling effects are severely restricted by the additional constraint arising from the integrability condition.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [SPIRES].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [SPIRES].
S. Cucu, H. Lü and J.F. Vazquez-Poritz, Interpolating from AdS(D-2) × S 2 to AdS(D), Nucl. Phys. B 677 (2004) 181 [hep-th/0304022] [SPIRES].
H. Lü, C.N. Pope and J.F. Vazquez-Poritz, From AdS black holes to supersymmetric flux-branes, Nucl. Phys. B 709 (2005) 47 [hep-th/0307001] [SPIRES].
J. Perz, P. Smyth, T. Van Riet and B. Vercnocke, First-order flow equations for extremal and non-extremal black holes, JHEP 03 (2009) 150 [arXiv:0810.1528] [SPIRES].
K. Skenderis and P.K. Townsend, Pseudo-supersymmetry and the domain-wall/cosmology correspondence, J. Phys. A 40 (2007) 6733 [hep-th/0610253] [SPIRES].
J. Grover, J.B. Gutowski, C.A.R. Herdeiro and W. Sabra, HKT Geometry and de Sitter Supergravity, Nucl. Phys. B 809 (2009) 406 [arXiv:0806.2626] [SPIRES].
J. Grover et al., Gauduchon-Tod structures, Sim holonomy and de Sitter supergravity, JHEP 07 (2009) 069 [arXiv:0905.3047] [SPIRES].
H. Lü, C.N. Pope and J. Rahmfeld, A construction of Killing spinors on S n, J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [SPIRES].
H. Lü, C.N. Pope and P.K. Townsend, Domain walls from anti-de Sitter spacetime, Phys. Lett. B 391 (1997) 39 [hep-th/9607164] [SPIRES].
H. Lü, C.N. Pope, E. Sezgin and K.S. Stelle, Stainless super p-branes, Nucl. Phys. B 456 (1995) 669 [hep-th/9508042] [SPIRES].
R. Güven, Black p-brane solutions of D = 11 supergravity theory, Phys. Lett. B 276 (1992) 49 [SPIRES].
G. Papadopoulos and P.K. Townsend, Intersecting M-branes, Phys. Lett. B 380 (1996) 273 [hep-th/9603087] [SPIRES].
A.A. Tseytlin, Harmonic superpositions of M-branes, Nucl. Phys. B 475 (1996) 149 [hep-th/9604035] [SPIRES].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, Systematics of IIB spinorial geometry, Class. Quant. Grav. 23 (2006) 1617 [hep-th/0507087] [SPIRES].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of type IIB supergravity, Class. Quant. Grav. 23 (2006) 4693 [hep-th/0510125] [SPIRES].
J.M. Figueroa-O’Farrill and G. Papadopoulos, Maximally supersymmetric solutions of ten-and eleven-dimensional supergravities, JHEP 03 (2003) 048 [hep-th/0211089] [SPIRES].
J.P. Gauntlett and S. Pakis, The geometry of D = 11 Killing spinors, JHEP 04 (2003) 039 [hep-th/0212008] [SPIRES].
J.B. Gutowski, D. Martelli and H.S. Reall, All supersymmetric solutions of minimal supergravity in six dimensions, Class. Quant. Grav. 20 (2003) 5049 [hep-th/0306235] [SPIRES].
J.T. Liu and D. Vaman, Bubbling 1/2 BPS solutions of minimal six-dimensional supergravity, Phys. Lett. B 642 (2006) 411 [hep-th/0412242] [SPIRES].
D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [SPIRES].
S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [SPIRES].
B. Chen et al., Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity, JHEP 10 (2007) 003 [arXiv:0704.2233] [SPIRES].
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ArXiv ePrint: 1103.0563
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Lü, H., Wang, ZL. Pseudo-Killing spinors, pseudo-supersymmetric p-branes, bubbling and less-bubbling AdS spaces. J. High Energ. Phys. 2011, 113 (2011). https://doi.org/10.1007/JHEP06(2011)113
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DOI: https://doi.org/10.1007/JHEP06(2011)113