Abstract
We find and classify the \( \mathcal{N}=1 \) SUSY multiplets on AdS4 which contain partially massless fields. We do this by studying the non-unitary representations of the d = 3 superconformal algebra of the boundary. The simplest super-multiplet which contains a partially massless spin-2 particle also contains a massless photon, a massless spin-3/2 particle and a massive spin-3/2 particle. The gauge parameters form a Wess-Zumino super-multiplet which contains the gauge parameters of the photon, the partially massless graviton, and the massless spin-3/2 particle. We find the AdS4 action and SUSY transformations for this multiplet. More generally, we classify new types of shortening conditions that can arise for non-unitary representations of the d = 3 superconformal algebra.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Deser and R.I. Nepomechie, Anomalous Propagation of Gauge Fields in Conformally Flat Spaces, Phys. Lett. B 132 (1983) 321 [INSPIRE].
S. Deser and R.I. Nepomechie, Gauge Invariance Versus Masslessness in de Sitter Space, Annals Phys. 154 (1984) 396 [INSPIRE].
A. Higuchi, Forbidden Mass Range for Spin-2 Field Theory in de Sitter Space-time, Nucl. Phys. B 282 (1987) 397 [INSPIRE].
L. Brink, R.R. Metsaev and M.A. Vasiliev, How massless are massless fields in AdS d, Nucl. Phys. B 586 (2000) 183 [hep-th/0005136] [INSPIRE].
S. Deser and A. Waldron, Gauge invariances and phases of massive higher spins in (A)dS, Phys. Rev. Lett. 87 (2001) 031601 [hep-th/0102166] [INSPIRE].
S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [INSPIRE].
S. Deser and A. Waldron, Stability of massive cosmological gravitons, Phys. Lett. B 508 (2001) 347 [hep-th/0103255] [INSPIRE].
S. Deser and A. Waldron, Null propagation of partially massless higher spins in (A)dS and cosmological constant speculations, Phys. Lett. B 513 (2001) 137 [hep-th/0105181] [INSPIRE].
Yu. M. Zinoviev, On massive high spin particles in AdS, hep-th/0108192 [INSPIRE].
E.D. Skvortsov and M.A. Vasiliev, Geometric formulation for partially massless fields, Nucl. Phys. B 756 (2006) 117 [hep-th/0601095] [INSPIRE].
N. Boulanger, C. Iazeolla and P. Sundell, Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism, JHEP 07 (2009) 013 [arXiv:0812.3615] [INSPIRE].
E.D. Skvortsov, Gauge fields in (A)dS(d) and Connections of its symmetry algebra, J. Phys. A 42 (2009) 385401 [arXiv:0904.2919] [INSPIRE].
K. Alkalaev and M. Grigoriev, Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type, Nucl. Phys. B 853 (2011) 663 [arXiv:1105.6111] [INSPIRE].
E. Joung, L. Lopez and M. Taronna, On the cubic interactions of massive and partially-massless higher spins in (A)dS, JHEP 07 (2012) 041 [arXiv:1203.6578] [INSPIRE].
T. Basile, X. Bekaert and N. Boulanger, Mixed-symmetry fields in de Sitter space: a group theoretical glance, JHEP 05 (2017) 081 [arXiv:1612.08166] [INSPIRE].
F.A. Dolan, On Superconformal Characters and Partition Functions in Three Dimensions, J. Math. Phys. 51 (2010) 022301 [arXiv:0811.2740] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for Superconformal Field Theories in 3,5 and 6 Dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, arXiv:1612.00809 [INSPIRE].
Y. Oshima and M. Yamazaki, Determinant Formula for Parabolic Verma Modules of Lie Superalgebras, J. Algebra 495 (2018) 51 [arXiv:1603.06705] [INSPIRE].
K. Sen and M. Yamazaki, Polology of Superconformal Blocks, arXiv:1810.01264 [INSPIRE].
C. Brust and K. Hinterbichler, Free □k scalar conformal field theory, JHEP 02 (2017) 066 [arXiv:1607.07439] [INSPIRE].
O. Malaeb, Massive Gravity with N = 1 local Supersymmetry, Eur. Phys. J. C 73 (2013) 2549 [arXiv:1302.5092] [INSPIRE].
O. Malaeb, Supersymmetrizing Massive Gravity, Phys. Rev. D 88 (2013) 025002 [arXiv:1303.3580] [INSPIRE].
F. Del Monte, D. Francia and P.A. Grassi, Multimetric Supergravities, JHEP 09 (2016) 064 [arXiv:1605.06793] [INSPIRE].
N.A. Ondo and A.J. Tolley, Deconstructing Supergravity: Massive Supermultiplets, JHEP 11 (2018) 082 [arXiv:1612.08752] [INSPIRE].
Y.M. Zinoviev, On massive super(bi)gravity in the constructive approach, Class. Quant. Grav. 35 (2018) 175006 [arXiv:1805.01650] [INSPIRE].
Yu. M. Zinoviev, On massive spin 2 interactions, Nucl. Phys. B 770 (2007) 83 [hep-th/0609170] [INSPIRE].
S.F. Hassan, A. Schmidt-May and M. von Strauss, On Partially Massless Bimetric Gravity, Phys. Lett. B 726 (2013) 834 [arXiv:1208.1797] [INSPIRE].
S.F. Hassan, A. Schmidt-May and M. von Strauss, Bimetric theory and partial masslessness with Lanczos-Lovelock terms in arbitrary dimensions, Class. Quant. Grav. 30 (2013) 184010 [arXiv:1212.4525] [INSPIRE].
C. de Rham and S. Renaux-Petel, Massive Gravity on de Sitter and Unique Candidate for Partially Massless Gravity, JCAP 01 (2013) 035 [arXiv:1206.3482] [INSPIRE].
S.F. Hassan, A. Schmidt-May and M. von Strauss, Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory, Universe 1 (2015) 92 [arXiv:1303.6940] [INSPIRE].
S. Deser, M. Sandora and A. Waldron, Nonlinear Partially Massless from Massive Gravity?, Phys. Rev. D 87 (2013) 101501 [arXiv:1301.5621] [INSPIRE].
C. de Rham, K. Hinterbichler, R.A. Rosen and A.J. Tolley, Evidence for and obstructions to nonlinear partially massless gravity, Phys. Rev. D 88 (2013) 024003 [arXiv:1302.0025] [INSPIRE].
Yu. M. Zinoviev, Massive spin-2 in the Fradkin-Vasiliev formalism. I. Partially massless case, Nucl. Phys. B 886 (2014) 712 [arXiv:1405.4065] [INSPIRE].
S. Garcia-Saenz and R.A. Rosen, A non-linear extension of the spin-2 partially massless symmetry, JHEP 05 (2015) 042 [arXiv:1410.8734] [INSPIRE].
K. Hinterbichler, Manifest Duality Invariance for the Partially Massless Graviton, Phys. Rev. D 91 (2015) 026008 [arXiv:1409.3565] [INSPIRE].
E. Joung, W. Li and M. Taronna, No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields, Phys. Rev. Lett. 113 (2014) 091101 [arXiv:1406.2335] [INSPIRE].
S. Alexandrov and C. Deffayet, On Partially Massless Theory in 3 Dimensions, JCAP 03 (2015) 043 [arXiv:1410.2897] [INSPIRE].
S.F. Hassan, A. Schmidt-May and M. von Strauss, Extended Weyl Invariance in a Bimetric Model and Partial Masslessness, Class. Quant. Grav. 33 (2016) 015011 [arXiv:1507.06540] [INSPIRE].
K. Hinterbichler and R.A. Rosen, Partially Massless Monopoles and Charges, Phys. Rev. D 92 (2015) 105019 [arXiv:1507.00355] [INSPIRE].
D. Cherney, S. Deser, A. Waldron and G. Zahariade, Non-linear duality invariant partially massless models?, Phys. Lett. B 753 (2016) 293 [arXiv:1511.01053] [INSPIRE].
S. Gwak, E. Joung, K. Mkrtchyan and S.-J. Rey, Rainbow Valley of Colored (Anti) de Sitter Gravity in Three Dimensions, JHEP 04 (2016) 055 [arXiv:1511.05220] [INSPIRE].
S. Gwak, E. Joung, K. Mkrtchyan and S.-J. Rey, Rainbow vacua of colored higher-spin (A)dS 3 gravity, JHEP 05 (2016) 150 [arXiv:1511.05975] [INSPIRE].
S. Garcia-Saenz, K. Hinterbichler, A. Joyce, E. Mitsou and R.A. Rosen, No-go for Partially Massless Spin-2 Yang-Mills, JHEP 02 (2016) 043 [arXiv:1511.03270] [INSPIRE].
K. Hinterbichler and A. Joyce, Manifest Duality for Partially Massless Higher Spins, JHEP 09 (2016) 141 [arXiv:1608.04385] [INSPIRE].
J. Bonifacio and K. Hinterbichler, Kaluza-Klein reduction of massive and partially massless spin-2 fields, Phys. Rev. D 95 (2017) 024023 [arXiv:1611.00362] [INSPIRE].
L. Apolo and S.F. Hassan, Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity, Class. Quant. Grav. 34 (2017) 105005 [arXiv:1609.09514] [INSPIRE].
L. Apolo, S.F. Hassan and A. Lundkvist, Gauge and global symmetries of the candidate partially massless bimetric gravity, Phys. Rev. D 94 (2016) 124055 [arXiv:1609.09515] [INSPIRE].
L. Bernard, C. Deffayet, K. Hinterbichler and M. von Strauss, Partially Massless Graviton on Beyond Einstein Spacetimes, Phys. Rev. D 95 (2017) 124036 [Erratum ibid. D 98 (2018) 069902] [arXiv:1703.02538] [INSPIRE].
N. Boulanger, C. Deffayet, S. Garcia-Saenz and L. Traina, Consistent deformations of free massive field theories in the Stueckelberg formulation, JHEP 07 (2018) 021 [arXiv:1806.04695] [INSPIRE].
X. Bekaert and M. Grigoriev, Higher order singletons, partially massless fields and their boundary values in the ambient approach, Nucl. Phys. B 876 (2013) 667 [arXiv:1305.0162] [INSPIRE].
T. Basile, X. Bekaert and N. Boulanger, Flato-Fronsdal theorem for higher-order singletons, JHEP 11 (2014) 131 [arXiv:1410.7668] [INSPIRE].
K.B. Alkalaev, M. Grigoriev and E.D. Skvortsov, Uniformizing higher-spin equations, J. Phys. A 48 (2015) 015401 [arXiv:1409.6507] [INSPIRE].
E. Joung and K. Mkrtchyan, Partially-massless higher-spin algebras and their finite-dimensional truncations, JHEP 01 (2016) 003 [arXiv:1508.07332] [INSPIRE].
C. Brust and K. Hinterbichler, Partially Massless Higher-Spin Theory, JHEP 02 (2017) 086 [arXiv:1610.08510] [INSPIRE].
Z. Maassarani and D. Serban, Nonunitary conformal field theory and logarithmic operators for disordered systems, Nucl. Phys. B 489 (1997) 603 [hep-th/9605062] [INSPIRE].
J. Penedones, E. Trevisani and M. Yamazaki, Recursion Relations for Conformal Blocks, JHEP 09 (2016) 070 [arXiv:1509.00428] [INSPIRE].
S.M. Carroll, Spacetime and geometry: An introduction to general relativity, Addison-Wesley, U.S.A., (2004), [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
G. Mack, All unitary ray representations of the conformal group SU(2, 2) with positive energy, Commun. Math. Phys. 55 (1977) 1 [INSPIRE].
J.C. Jantzen, Kontravariante formen auf induzierten darstellungen halbeinfacher lie-algebren, Math. Ann. 226 (1977) 53.
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 783 [hep-th/9712074] [INSPIRE].
L. Dolan, C.R. Nappi and E. Witten, Conformal operators for partially massless states, JHEP 10 (2001) 016 [hep-th/0109096] [INSPIRE].
B. de Wit and I. Herger, Anti-de Sitter supersymmetry, Lect. Notes Phys. 541 (2000) 79 [hep-th/9908005] [INSPIRE].
D. Simmons-Duffin, The Conformal Bootstrap, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015): Boulder, CO, U.S.A., June 1-26, 2015, pp. 1-74, arXiv:1602.07982 [INSPIRE].
T. Basile, X. Bekaert and E. Joung, Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra, arXiv:1808.07728 [INSPIRE].
P.A.M. Dirac, A remarkable representation of the 3 + 2 de Sitter group, J. Math. Phys. 4 (1963) 901 [INSPIRE].
V. Balasubramanian, P. Kraus and A.E. Lawrence, Bulk versus boundary dynamics in anti-de Sitter space-time, Phys. Rev. D 59 (1999) 046003 [hep-th/9805171] [INSPIRE].
C. De Rham, K. Hinterbichler and L.A. Johnson, On the (A)dS Decoupling Limits of Massive Gravity, JHEP 09 (2018) 154 [arXiv:1807.08754] [INSPIRE].
I.L. Buchbinder, S.J. Gates Jr., W.D. Linch, III and J. Phillips, New 4-D, N = 1 superfield theory: Model of free massive superspin 3/2 multiplet, Phys. Lett. B 535 (2002) 280 [hep-th/0201096] [INSPIRE].
Yu. M. Zinoviev, Massive spin two supermultiplets, hep-th/0206209 [INSPIRE].
R. Haag, J.T. Lopuszanski and M. Sohnius, All Possible Generators of Supersymmetries of the s Matrix, Nucl. Phys. B 88 (1975) 257 [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K., (2012).
S.M. Kuzenko and A.G. Sibiryakov, Free massless higher superspin superfields on the anti-de Sitter superspace, Phys. Atom. Nucl. 57 (1994) 1257 [Yad. Fiz. 57 (1994) 1326] [arXiv:1112.4612] [INSPIRE].
I.L. Buchbinder, S.M. Kuzenko and A.G. Sibiryakov, Quantization of higher spin superfields in the anti-de Sitter superspace, Phys. Lett. B 352 (1995) 29 [hep-th/9502148] [INSPIRE].
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of Conformal Supergravity, Phys. Rev. D 17 (1978) 3179 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept. 119 (1985) 233 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
Yu. M. Zinoviev, Massive supermultiplets with spin 3/2, JHEP 05 (2007) 092 [hep-th/0703118] [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: 1810.01881
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Garcia-Saenz, S., Hinterbichler, K. & Rosen, R.A. Supersymmetric partially massless fields and non-unitary superconformal representations. J. High Energ. Phys. 2018, 166 (2018). https://doi.org/10.1007/JHEP11(2018)166
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)166