Abstract
IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional ‘dual graviton’. The invariant E6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions for the USp(8) covariant fermion fields. Implications are discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. de Wit and H. Nicolai, d = 11 supergravity with local SU(8) invariance, Nucl. Phys. B 274 (1986) 363 [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].
H. Nicolai and K. Pilch, Consistent truncation of D = 11 supergravity on AdS 4 × S 7, JHEP 03 (2012) 099 [arXiv:1112.6131] [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].
H. Godazgar, M. Godazgar and H. Nicolai, Testing the non-linear flux ansatz for maximal supergravity, Phys. Rev. D 87 (2013) 085038 [arXiv:1303.1013] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Generalised geometry from the ground up, JHEP 02 (2014) 075 [arXiv:1307.8295] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Nonlinear Kaluza-Klein theory for dual fields, Phys. Rev. D 88 (2013) 125002 [arXiv:1309.0266] [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, The maximal D = 5 supergravities, Nucl. Phys. B 716 (2005) 215 [hep-th/0412173] [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].
B. de Wit, H. Nicolai and H. Samtleben, Gauged supergravities, tensor hierarchies and M-theory, JHEP 02 (2008) 044 [arXiv:0801.1294] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory I: E 6(6) covariant form of M-theory and type IIB, Phys. Rev. D 89 (2014) 066016 [arXiv:1312.0614] [INSPIRE].
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099] [INSPIRE].
M. Gualtieri, Generalized complex geometry, math/0401221 [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
C.M. Hull, Generalised geometry for M-theory, JHEP 07 (2007) 079 [hep-th/0701203] [INSPIRE].
C. Hull and B. Zwiebach, Double field theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
D.S. Berman and M.J. Perry, Generalized geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
O. Hohm and S.K. Kwak, Frame-like geometry of double field theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as generalised geometry I: type II theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].
D.S. Berman, H. Godazgar, M.J. Perry and P. West, Duality invariant actions and generalised geometry, JHEP 02 (2012) 108 [arXiv:1111.0459] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, arXiv:1401.3360 [INSPIRE].
P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].
T. Damour, M. Henneaux and H. Nicolai, E 10 and a ‘small tension expansion’ of M-theory, Phys. Rev. Lett. 89 (2002) 221601 [hep-th/0207267] [INSPIRE].
T. Damour, A. Kleinschmidt and H. Nicolai, K(E 10), supergravity and fermions, JHEP 08 (2006) 046 [hep-th/0606105] [INSPIRE].
P. West, Generalised geometry, eleven dimensions and E 11, JHEP 02 (2012) 018 [arXiv:1111.1642] [INSPIRE].
C. Hillmann, Generalized E 7(7) coset dynamics and D = 11 supergravity, JHEP 03 (2009) 135 [arXiv:0901.1581] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional form of D = 11 supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
J.H. Schwarz and P.C. West, Symmetries and transformations of chiral N = 2 D = 10 supergravity, Phys. Lett. B 126 (1983) 301 [INSPIRE].
J.H. Schwarz, Covariant field equations of chiral N = 2 D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].
P.S. Howe and P.C. West, The complete N = 2, D = 10 supergravity, Nucl. Phys. B 238 (1984) 181 [INSPIRE].
E. Cremmer, Supergravities in five dimensions, in Superspace and supergravity, S.W. Hawking and M. Roček eds., Cambridge University Press, Cambridge U.K. (1981), reprinted in Supergravities in diverse dimensions, A. Salam and E. Sezgin eds., North-Holland/World Scientific (1989) 422.
M. Günaydin, L.J. Romans and N.P. Warner, Compact and noncompact gauged supergravity theories in five dimensions, Nucl. Phys. B 272 (1986) 598 [INSPIRE].
K. Pilch and N.P. Warner, N = 2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [INSPIRE].
E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
T. Curtright, Generalized gauge fields, Phys. Lett. B 165 (1985) 304 [INSPIRE].
C.M. Hull, Duality in gravity and higher spin gauge fields, JHEP 09 (2001) 027 [hep-th/0107149] [INSPIRE].
X. Bekaert, N. Boulanger and M. Henneaux, Consistent deformations of dual formulations of linearized gravity: a no go result, Phys. Rev. D 67 (2003) 044010 [hep-th/0210278] [INSPIRE].
H. Godazgar, M. Godazgar and H. Nicolai, Embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions, Phys. Rev. D 89 (2014) 045009 [arXiv:1312.1061] [INSPIRE].
O. Hohm and H. Samtleben, Consistent Kaluza-Klein truncations via exceptional field theory, JHEP 01 (2015) 131 [arXiv:1410.8145] [INSPIRE].
G. Dall’Agata, K. Lechner and D.P. Sorokin, Covariant actions for the bosonic sector of D=10 IIB supergravity,Class. Quant. Grav. 14 (1997) L195 [hep-th/9707044] [INSPIRE].
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 D=10 supergravity on S 5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
M. Günaydin and N. Marcus, The spectrum of the S 5 compactification of the chiral N = 2, D=10 supergravity and the unitary supermultiplets of U(2,2/4),Class. Quant. Grav. 2 (1985) L11 [INSPIRE].
B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].
B. de Wit and H. Nicolai, On the relation between D = 4 and D = 11 supergravity, Nucl. Phys. B 243 (1984) 91 [INSPIRE].
B. de Wit, H. Nicolai and N.P. Warner, The embedding of gauged N = 8 supergravity into D=11 supergravity,Nucl. Phys. B 255 (1985) 29 [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: 1412.8297
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
Ciceri, F., de Wit, B. & Varela, O. IIB supergravity and the E6(6) covariant vector-tensor hierarchy. J. High Energ. Phys. 2015, 94 (2015). https://doi.org/10.1007/JHEP04(2015)094
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)094