Abstract
We present f (R) theories of ten-dimensional supergravities, up to and including the quadratic order in fermion fields in action. They are obtained by performing the conformal scaling on the usual supergravities to the f (R) frame in which the dilaton becomes an auxiliary field and can be integrated out. The f (R) frame coincides with that of M-theory, D2-branes or NS-NS 5-branes. We study various BPS p-brane solutions and their near-horizon AdS × sphere geometries in the context of the f (R) theories. We find that new solutions emerge with global structures that do not exist in the corresponding solutions of the original supergravity description. In lower dimensions, We construct the f (R) theory of \(\mathcal{N} = 2\), D = 5 gauged supergravity with a vector multiplet, and that for the four-dimensional U(1)4 gauged theory with three vector fields set equal. We find that some previously-known BPS singular “superstars” become wormholes in the f (R) theories. We also construct a large class of f (R) (gauged) pseudo-supergravities. In addition we show that the breathing mode in the Kaluza-Klein reduction of Gauss-Bonnet gravity on S 1 is an auxiliary field and can be integrated out.
Similar content being viewed by others
References
K. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
K. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [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].
H. Lü and C. Pope, Critical gravity in four dimensions, Phys. Rev. Lett. 106 (2011) 181302 [arXiv:1101.1971] [INSPIRE].
H. Lü, Y. Pang and C. Pope, Conformal gravity and extensions of critical gravity, Phys. Rev. D 84 (2011) 064001 [arXiv:1106.4657] [INSPIRE].
S. Nojiri and S.D. Odintsov, Introduction to modified gravity and gravitational alternative for dark energy, eConf C 0602061 (2006) 06 [hep-th/0601213] [INSPIRE].
T.P. Sotiriou and V. Faraoni, f (R) theories of gravity, Rev. Mod. Phys. 82 (2010) 451 [arXiv:0805.1726] [INSPIRE].
A. De Felice and S. Tsujikawa, f (R) theories, Living Rev. Rel. 13 (2010) 3 [arXiv:1002.4928] [INSPIRE].
H. Liu, H. Lü and Z.-L. Wang, f (R) Gravities, Killing spinor equations, “BPS” domain walls and cosmology, JHEP 02 (2012) 083 [arXiv:1111.6602] [INSPIRE].
H. Lü, C. Pope and Z.-L. Wang, Pseudo-supersymmetry, consistent sphere reduction and Killing spinors for the bosonic string, Phys. Lett. B 702 (2011) 442 [arXiv:1105.6114] [INSPIRE].
H. Lü and Z.-L. Wang, Killing spinors for the bosonic string, Europhys. Lett. 97 (2012) 50010 [arXiv:1106.1664] [INSPIRE].
H. Liu, H. Lü and Z.-L. Wang, Killing spinors for the bosonic string and the Kaluza-Klein theory with scalar potentials, Eur. Phys. J. C 72 (2012) 1853 [arXiv:1106.4566] [INSPIRE].
H. Lü, C. Pope and Z.-L. Wang, Pseudo-supergravity extension of the bosonic string, Nucl. Phys. B 854 (2012) 293 [arXiv:1106.5794] [INSPIRE].
H.-S. Liu, H. Lü, Z.-L. Wang, H. Lü and Z.-L. Wang, Gauged Kaluza-Klein AdS pseudo-supergravity, Phys. Lett. B 703 (2011) 524 [arXiv:1107.2659] [INSPIRE].
G.J. Olmo, Limit to general relativity in f (R) theories of gravity, Phys. Rev. D 75 (2007) 023511 [gr-qc/0612047] [INSPIRE].
L. Romans, Massive \(\mathcal{N} = 2a\) supergravity in ten-dimensions, Phys. Lett. B 169 (1986) 374 [INSPIRE].
D.Z. Freedman and J.H. Schwarz, \(\mathcal{N} = 4\) supergravity theory with local SU(2) × SU(2) invariance, Nucl. Phys. B 137 (1978) 333 [INSPIRE].
A. Salam and E. Sezgin, Chiral compactification on Minkowski ×S 2 of \(\mathcal{N} = 2\) Einstein-Maxwell supergravity in six-dimensions, Phys. Lett. B 147 (1984) 47 [INSPIRE].
A.H. Chamseddine and W. Sabra, D = 7 SU(2) gauged supergravity from D = 10 supergravity, Phys. Lett. B 476 (2000) 415 [hep-th/9911180] [INSPIRE].
M. Cvetič, G. Gibbons, H. Lü and C. Pope, Consistent group and coset reductions of the bosonic string, Class. Quant. Grav. 20 (2003) 5161 [hep-th/0306043] [INSPIRE].
H. Lü, C. Pope, E. Sezgin and K. Stelle, Stainless super p-branes, Nucl. Phys. B 456 (1995) 669 [hep-th/9508042] [INSPIRE].
M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
L. Romans, The F 4 gauged supergravity in six dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
M. Cvetič, S. Gubser, H. Lü and C. 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].
Z.-W. Chong, H. Lü and C. Pope, BPS geometries and AdS bubbles, Phys. Lett. B 614 (2005) 96 [hep-th/0412221] [INSPIRE].
E. Cremmer, B. Julia and J. Scherk, Supergravity theory in eleven-dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].
E. Bergshoeff, M. de Roo, B. de Wit and P. van Nieuwenhuizen, Ten-dimensional Maxwell-Einstein supergravity, its currents and the issue of its auxiliary fields, Nucl. Phys. B 195 (1982) 97 [INSPIRE].
M. Duff, R.R. Khuri and J. Lu, String solitons, Phys. Rept. 259 (1995) 213 [hep-th/9412184] [INSPIRE].
H. Lü, C. Pope and P. Townsend, Domain walls from anti-de Sitter space-time, Phys. Lett. B 391 (1997) 39 [hep-th/9607164] [INSPIRE].
D. Youm, Localized intersecting BPS branes, hep-th/9902208 [INSPIRE].
I. Campbell and P.C. West, \(\mathcal{N} = 2\) D = 10 Nonchiral supergravity and its spontaneous compactification, Nucl. Phys. B 243 (1984) 112 [INSPIRE].
G. Gibbons, G.T. Horowitz and P. Townsend, Higher dimensional resolution of dilatonic black hole singularities, Class. Quant. Grav. 12 (1995) 297 [hep-th/9410073] [INSPIRE].
G.W. Gibbons, M.B. Green and M.J. Perry, Instantons and seven-branes in type IIB superstring theory, Phys. Lett. B 370 (1996) 37 [hep-th/9511080] [INSPIRE].
J.H. Schwarz, Covariant field equations of chiral \(\mathcal{N} = 2\) D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].
E. Bergshoeff, C.M. Hull and T. Ortín, Duality in the type-II superstring effective action, Nucl. Phys. B 451 (1995) 547 [hep-th/9504081] [INSPIRE].
H. Lü, C. Pope and T.A. Tran, Five-dimensional \(\mathcal{N} = 2\vartriangle\) , SU(2) × U(1) gauged supergravity from type IIB, Phys. Lett. B 475 (2000) 261 [hep-th/9909203] [INSPIRE].
A. Brandhuber and Y. Oz, The D4-D8 brane system and five-dimensional fixed points, Phys. Lett. B 460 (1999) 307 [hep-th/9905148] [INSPIRE].
M. Cvetič, H. Lü and C. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett. 83 (1999) 5226 [hep-th/9906221] [INSPIRE].
Z. Chong, H. Lü and C. Pope, Rotating strings in massive type IIA supergravity, hep-th/0402202 [INSPIRE].
A.H. Chamseddine and H. Nicolai, Coupling the SO(2) supergravity through dimensional reduction, Phys. Lett. B 96 (1980) 89 [INSPIRE].
M. Günaydin, G. Sierra and P. Townsend, Gauging the D = 5 Maxwell-Einstein supergravity theories: more on Jordan algebras, Nucl. Phys. B 253 (1985) 573 [INSPIRE].
K. Behrndt, A.H. Chamseddine and W. Sabra, BPS black holes in \(\mathcal{N} = 2\) five-dimensional AdS supergravity, Phys. Lett. B 442 (1998) 97 [hep-th/9807187] [INSPIRE].
K. Behrndt, M. Cvetič and W. Sabra, Nonextreme black holes of five-dimensional \(\mathcal{N} = 2\) AdS supergravity, Nucl. Phys. B 553 (1999) 317 [hep-th/9810227] [INSPIRE].
M. Duff and J.T. Liu, Anti-de Sitter black holes in gauged \(\mathcal{N} = 8\) supergravity, Nucl. Phys. B 554 (1999) 237 [hep-th/9901149] [INSPIRE].
W. Sabra, Anti-de Sitter BPS black holes in \(\mathcal{N} = 2\) gauged supergravity, Phys. Lett. B 458 (1999) 36 [hep-th/9903143] [INSPIRE].
A. Van Proeyen, Tools for supersymmetry, hep-th/9910030 [INSPIRE].
E. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
S.-Q. Wu, General rotating charged Kaluza-Klein AdS black holes in higher dimensions, Phys. Rev. D 83 (2011) 121502 [arXiv:1108.4157] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1201.2417
Rights and permissions
About this article
Cite this article
Liu, H., Lü, H. & Wang, ZL. f (R) Theories of supergravities and pseudo-supergravities. J. High Energ. Phys. 2012, 72 (2012). https://doi.org/10.1007/JHEP04(2012)072
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2012)072