Abstract
We develop a formalism to construct supersymmetric backgrounds within the superspace formulation for five-dimensional (5D) conformal supergravity given in arXiv:0802.3953. Our approach is applicable to any off-shell formulation for 5D minimal Poincaré and anti-de Sitter supergravity theories realized as the Weyl multiplet coupled with two compensators. For those superspace backgrounds which obey the equations of motion for (gauged) supergravity, we naturally reproduce the supersymmetric solutions constructed a decade ago by Gauntlett et al. For certain supersymmetric backgrounds with eight supercharges, we construct a large family of off-shell supersymmetric sigma models such that the superfield Lagrangian is given in terms of the Kähler potential of a real analytic Kähler manifold.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Five-dimensional superfield supergravity, Phys. Lett. B 661 (2008) 42 [arXiv:0710.3440] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, 5D supergravity and projective superspace, JHEP 02 (2008) 004 [arXiv:0712.3102] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Super-Weyl invariance in 5D supergravity, JHEP 04 (2008) 032 [arXiv:0802.3953] [INSPIRE].
M. Zucker, Minimal off-shell supergravity in five-dimensions, Nucl. Phys. B 570 (2000) 267 [hep-th/9907082] [INSPIRE].
M. Zucker, Gauged N = 2 off-shell supergravity in five-dimensions, JHEP 08 (2000) 016 [hep-th/9909144] [INSPIRE].
M. Zucker, Off-shell supergravity in five-dimensions and supersymmetric brane world scenarios, Fortsch. Phys. 51 (2003) 899 [INSPIRE].
T. Kugo and K. Ohashi, Supergravity tensor calculus in 5D from 6D, Prog. Theor. Phys. 104 (2000) 835 [hep-ph/0006231] [INSPIRE].
T. Kugo and K. Ohashi, Off-shell d = 5 supergravity coupled to matter Yang-Mills system, Prog. Theor. Phys. 105 (2001) 323 [hep-ph/0010288] [INSPIRE].
T. Fujita and K. Ohashi, Superconformal tensor calculus in five-dimensions, Prog. Theor. Phys. 106 (2001) 221 [hep-th/0104130] [INSPIRE].
E. Bergshoeff et al., Weyl multiplets of N = 2 conformal supergravity in five-dimensions, JHEP 06 (2001) 051 [hep-th/0104113] [INSPIRE].
E. Bergshoeff et al., Superconformal N = 2, D = 5 matter with and without actions, JHEP 10 (2002) 045 [hep-th/0205230] [INSPIRE].
E. Bergshoeff et al., N = 2 supergravity in five-dimensions revisited, Class. Quant. Grav. 21 (2004) 3015 [hep-th/0403045] [INSPIRE].
P.S. Howe, Off-shell N=2 and N=4 supergravity in five-dimensions, in: Quantum Structure of Space and Time, M.J. Duff and C.J. Isham eds., Cambridge University Press, Cambridge U.K. (1982), pg. 239.
P.S. Howe and U. Lindström, The supercurrent in five-dimensions, Phys. Lett. B 103 (1981) 422 [INSPIRE].
S.M. Kuzenko, On compactified harmonic/projective superspace, 5D superconformal theories and all that, Nucl. Phys. B 745 (2006) 176 [hep-th/0601177] [INSPIRE].
U. Lindström and M. Roček, New hyperKähler metrics and new supermultiplets, Commun. Math. Phys. 115 (1988) 21 [INSPIRE].
U. Lindström and M. Roček, N = 2 super Yang-Mills theory in projective superspace, Commun. Math. Phys. 128 (1990) 191 [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Five-dimensional N = 1 AdS superspace: geometry, off-shell multiplets and dynamics, Nucl. Phys. B 785 (2007) 34 [arXiv:0704.1185] [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity or a Walk Through Superspace, IOP, Bristol U.K. (1995).
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Field theory in 4D N = 2 conformally flat superspace, JHEP 10 (2008) 001 [arXiv:0807.3368] [INSPIRE].
D. Butter and S.M. Kuzenko, N = 2 supersymmetric σ-models in AdS, Phys. Lett. B 703 (2011) 620 [arXiv:1105.3111] [INSPIRE].
D. Butter and S.M. Kuzenko, The structure of N = 2 supersymmetric nonlinear σ-models in AdS 4, JHEP 11 (2011) 080 [arXiv:1108.5290] [INSPIRE].
D. Butter, S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Extended supersymmetric σ-models in AdS 4 from projective superspace, JHEP 05 (2012) 138 [arXiv:1203.5001] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 (AdS) supergravity and associated supercurrents, JHEP 12 (2011) 052 [arXiv:1109.0496] [INSPIRE].
S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Three-dimensional (p,q) AdS superspaces and matter couplings, JHEP 08 (2012) 024 [arXiv:1205.4622] [INSPIRE].
D. Butter, S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Nonlinear σ-models with AdS supersymmetry in three dimensions, JHEP 02 (2013) 121 [arXiv:1210.5906] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
B. Jia and E. Sharpe, Rigidly supersymmetric gauge theories on curved superspace, JHEP 04 (2012) 139 [arXiv:1109.5421] [INSPIRE].
H. Samtleben and D. Tsimpis, Rigid supersymmetric theories in 4d Riemannian space, JHEP 05 (2012) 132 [arXiv:1203.3420] [INSPIRE].
C. Klare, A. Tomasiello and A. Zaffaroni, Supersymmetry on curved spaces and holography, JHEP 08 (2012) 061 [arXiv:1205.1062] [INSPIRE].
T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring curved superspace, JHEP 08 (2012) 141 [arXiv:1205.1115] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact terms, unitarity and F-maximization in three-dimensional superconformal theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-simons contact terms in three dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [INSPIRE].
D. Cassani, C. Klare, D. Martelli, A. Tomasiello and A. Zaffaroni, Supersymmetry in Lorentzian curved spaces and holography, Commun. Math. Phys. 327 (2014) 577 [arXiv:1207.2181] [INSPIRE].
J.T. Liu, L.A. Pando Zayas and D. Reichmann, Rigid supersymmetric backgrounds of minimal off-shell supergravity, JHEP 10 (2012) 034 [arXiv:1207.2785] [INSPIRE].
T.T. Dumitrescu and G. Festuccia, Exploring curved superspace (II), JHEP 01 (2013) 072 [arXiv:1209.5408] [INSPIRE].
A. Kehagias and J.G. Russo, Global supersymmetry on curved spaces in various dimensions, Nucl. Phys. B 873 (2013) 116 [arXiv:1211.1367] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, Supersymmetric field theories on three-manifolds, JHEP 05 (2013) 017 [arXiv:1212.3388] [INSPIRE].
K. Hristov, A. Tomasiello and A. Zaffaroni, Supersymmetry on three-dimensional Lorentzian curved spaces and black hole holography, JHEP 05 (2013) 057 [arXiv:1302.5228] [INSPIRE].
P. de Medeiros and S. Hollands, Conformal symmetry superalgebras, Class. Quant. Grav. 30 (2013) 175016 [arXiv:1302.7269] [INSPIRE].
P. de Medeiros and S. Hollands, Superconformal quantum field theory in curved spacetime, Class. Quant. Grav. 30 (2013) 175015 [arXiv:1305.0499] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, The geometry of supersymmetric partition functions, JHEP 01 (2014) 124 [arXiv:1309.5876] [INSPIRE].
N.S. Deger, A. Kaya, H. Samtleben and E. Sezgin, Supersymmetric warped AdS in extended topologically massive supergravity, Nucl. Phys. B 884 (2014) 106 [arXiv:1311.4583] [INSPIRE].
C. Closset and S. Cremonesi, Comments on \( \mathcal{N}=\left(2,2\right) \) supersymmetry on two-manifolds, JHEP 07 (2014) 075 [arXiv:1404.2636] [INSPIRE].
S.M. Kuzenko, Symmetries of curved superspace, JHEP 03 (2013) 024 [arXiv:1212.6179] [INSPIRE].
S.M. Kuzenko, U. Lindström, M. Roček, I. Sachs and G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 supergravity theories: from superspace to components, Phys. Rev. D 89 (2014) 085028 [arXiv:1312.4267] [INSPIRE].
S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Off-shell supergravity-matter couplings in three dimensions, JHEP 03 (2011) 120 [arXiv:1101.4013] [INSPIRE].
S.M. Kuzenko and W.D. Linch III, On five-dimensional superspaces, JHEP 02 (2006) 038 [hep-th/0507176] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Conformally flat supergeometry in five dimensions, JHEP 06 (2008) 097 [arXiv:0804.1219] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).
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] [INSPIRE].
H. Stephani, D. Kramer, M. MacCullum, C. Hoenselaers and E. Hertl, Exact Solutions of Einstein’s Field Equations, second edition, Cambridge University Press, Cambridge U.K. (2003).
T. Ortin, Gravity and Strings, Cambridge University Press, Cambridge U.K. (2004).
B. de Wit, R. Philippe and A. Van Proeyen, The improved tensor multiplet in N = 2 supergravity, Nucl. Phys. B 219 (1983) 143 [INSPIRE].
U. Lindström and M. Roček, Scalar tensor duality and N = 1, N = 2 Nonlinear σ-models, Nucl. Phys. B 222 (1983) 285 [INSPIRE].
D. Butter and S.M. Kuzenko, New higher-derivative couplings in 4D N = 2 supergravity, JHEP 03 (2011) 047 [arXiv:1012.5153] [INSPIRE].
D. Butter and S.M. Kuzenko, N = 2 AdS supergravity and supercurrents, JHEP 07 (2011) 081 [arXiv:1104.2153] [INSPIRE].
S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].
J.P. Gauntlett and J.B. Gutowski, All supersymmetric solutions of minimal gauged supergravity in five-dimensions, Phys. Rev. D 68 (2003) 105009 [Erratum ibid. D 70 (2004) 089901] [hep-th/0304064] [INSPIRE].
J. Bagger and C. Xiong, AdS 5 supersymmetry in N = 1 superspace, JHEP 07 (2011) 119 [arXiv:1105.4852] [INSPIRE].
J. Bagger and J. Li, Supersymmetric nonlinear σ-model in AdS 5, Phys. Lett. B 702 (2011) 291 [arXiv:1106.2343] [INSPIRE].
N.J. Hitchin, A. Karlhede, U. Lindström and M. Roček, HyperKähler metrics and supersymmetry, Commun. Math. Phys. 108 (1987) 535 [INSPIRE].
L. Álvarez-Gaumé and D.Z. Freedman, Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model, Commun. Math. Phys. 80 (1981) 443 [INSPIRE].
C.M. Hull, A. Karlhede, U. Lindström and M. Roček, Nonlinear σ models and their gauging in and out of superspace, Nucl. Phys. B 266 (1986) 1 [INSPIRE].
S.M. Kuzenko, Projective superspace as a double punctured harmonic superspace, Int. J. Mod. Phys. A 14 (1999) 1737 [hep-th/9806147] [INSPIRE].
S.J. Gates Jr. and S.M. Kuzenko, The CNM hypermultiplet nexus, Nucl. Phys. B 543 (1999) 122 [hep-th/9810137] [INSPIRE].
S.J. Gates Jr. and S.M. Kuzenko, 4D, N = 2 supersymmetric off-shell σ-models on the cotangent bundles of Kähler manifolds, Fortsch. Phys. 48 (2000) 115 [hep-th/9903013] [INSPIRE].
D. Kaledin, Hyperkähler structures on total spaces of holomorphic cotangent bundles, in Hyperkähler Manifolds, D. Kaledin and M. Verbitsky eds., International Press, Cambridge U.S.A. (1999) [alg-geom/9710026].
D. Kaledin, A canonical hyperkähler metric on the total space of a cotangent bundle, in Quaternionic Structures in Mathematics and Physics, S. Marchiafava, P. Piccinni and M. Pontecorvo eds., World Scientific, Singapore (2001) [alg-geom/0011256].
B. Feix, Hyperkähler metrics on cotangent bundles, J. Reine Angew. Math. 532 (2001) 33.
Y. Pan, Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry, JHEP 05 (2014) 041 [arXiv:1308.1567] [INSPIRE].
Y. Imamura and H. Matsuno, Supersymmetric backgrounds from 5d \( \mathcal{N}=1 \) supergravity, JHEP 07 (2014) 055 [arXiv:1404.0210] [INSPIRE].
S. Deser, Scale invariance and gravitational coupling, Annals Phys. 59 (1970) 248 [INSPIRE].
S.M. Kuzenko, Symmetries of curved superspace, talk given at the Second ANZAMP Meeting, Mooloolaba Australia, 27–29 November 2013.
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: 1406.0727
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
Kuzenko, S.M., Novak, J. & Tartaglino-Mazzucchelli, G. Symmetries of curved superspace in five dimensions. J. High Energ. Phys. 2014, 175 (2014). https://doi.org/10.1007/JHEP10(2014)175
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2014)175