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Deconstructing supergravity: massive supermultiplets. (English) Zbl 1404.83138

Summary: Given the success of the deconstruction program in obtaining ghost-free massive gravity from 5-D Einstein gravity, we propose a modification of the deconstruction procedure that incorporates supersymmetry at the linear level. We discuss the relevant limits of a conjectured interacting theory of a massive spin 2 supermultiplet, and determine the linear theory to be the \( \mathcal{N}=1 \) Zinoviev theory, a supersymmetric extension of Fierz-Pauli theory. We develop a family of 1-site deconstruction procedures for fermionic fields (yielding Dirac and Majorana mass terms). The deconstruction procedure appropriate for giving fermions a Dirac mass is found to preserve half of the supersymmetry of the 5-D theory. We explicitly check this by deconstructing 5-D \( \mathcal{N}=2 \) super-Maxwell theory down to 4-D \( \mathcal{N}=1 \) super-Proca theory, and deconstructing linear 5-D \( \mathcal{N}=2 \) supergravity down to 4-D \( \mathcal{N}=1 \) Zinoviev theory, and derive the full 4-D supersymmetry algebras and Stückelberg symmetries from the 5-D superalgebras and gauge symmetries, respectively. We conjecture that this procedure should admit a generalization to fully non-linear theories.

MSC:

83E50 Supergravity
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

References:

[1] C. de Rham and G. Gabadadze, Selftuned Massive Spin-2, Phys. Lett.B 693 (2010) 334 [arXiv:1006.4367] [INSPIRE].
[2] C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev.D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
[3] Rham, C.; Gabadadze, G.; Tolley, AJ, Resummation of Massive Gravity, Phys. Rev. Lett., 106, 231101, (2011) · doi:10.1103/PhysRevLett.106.231101
[4] S.F. Hassan and R.A. Rosen, Resolving the Ghost Problem in non-Linear Massive Gravity, Phys. Rev. Lett.108 (2012) 041101 [arXiv:1106.3344] [INSPIRE].
[5] Rham, C., Massive Gravity, Living Rev. Rel., 17, 7, (2014) · Zbl 1320.83018 · doi:10.12942/lrr-2014-7
[6] A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev.D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
[7] C. de Rham, G. Gabadadze, L. Heisenberg and D. Pirtskhalava, Nonrenormalization and naturalness in a class of scalar-tensor theories, Phys. Rev.D 87 (2013) 085017 [arXiv:1212.4128] [INSPIRE].
[8] C. de Rham, L. Heisenberg and R.H. Ribeiro, Quantum Corrections in Massive Gravity, Phys. Rev.D 88 (2013) 084058 [arXiv:1307.7169] [INSPIRE].
[9] Cheung, C.; Remmen, GN, Positive Signs in Massive Gravity, JHEP, 04, 002, (2016) · Zbl 1388.83576
[10] L. Keltner and A.J. Tolley, UV properties of Galileons: Spectral Densities, arXiv:1502.05706 [INSPIRE].
[11] Yu.M. Zinoviev, Massive spin two supermultiplets, hep-th/0206209 [INSPIRE].
[12] O. Malaeb, Massive Gravity with N = 1 local Supersymmetry, Eur. Phys. J.C 73 (2013) 2549 [arXiv:1302.5092] [INSPIRE].
[13] O. Malaeb, Supersymmetrizing Massive Gravity, Phys. Rev.D 88 (2013) 025002 [arXiv:1303.3580] [INSPIRE].
[14] Chamseddine, AH; Mukhanov, V., Higgs for Graviton: Simple and Elegant Solution, JHEP, 08, 011, (2010) · Zbl 1291.81431 · doi:10.1007/JHEP08(2010)011
[15] F. Del Monte, D. Francia and P.A. Grassi, Multimetric Supergravities, JHEP09 (2016) 064 [arXiv:1605.06793] [INSPIRE]. · Zbl 1390.83392
[16] Zinoviev, YM, On massive super(bi)gravity in the constructive approach, Class. Quant. Grav., 35, 175006, (2018) · Zbl 1409.83216 · doi:10.1088/1361-6382/aad1fb
[17] S. Garcia-Saenz, K. Hinterbichler and R.A. Rosen, Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations, arXiv:1810.01881 [INSPIRE]. · Zbl 1404.81255
[18] Fierz, M.; Pauli, W., On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond., A173, 211, (1939) · JFM 65.1532.01 · doi:10.1098/rspa.1939.0140
[19] Fierz, M., Force-free particles with any spin, Helv. Phys. Acta, 12, 3, (1939) · Zbl 0020.18904 · doi:10.1002/hlca.19390220102
[20] H. van Dam and M.J.G. Veltman, Massive and massless Yang-Mills and gravitational fields, Nucl. Phys.B 22 (1970) 397 [INSPIRE].
[21] Zakharov, VI, Linearized gravitation theory and the graviton mass, JETP Lett., 12, 312, (1970)
[22] A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett.B 39 (1972) 393 [INSPIRE].
[23] E. Babichev and C. Deffayet, An introduction to the Vainshtein mechanism, Class. Quant. Grav.30 (2013) 184001 [arXiv:1304.7240] [INSPIRE]. · Zbl 1277.83002
[24] D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev.D 6 (1972) 3368 [INSPIRE].
[25] Creminelli, P.; Nicolis, A.; Papucci, M.; Trincherini, E., Ghosts in massive gravity, JHEP, 09, 003, (2005) · doi:10.1088/1126-6708/2005/09/003
[26] C. Aragone and S. Deser, Constraints on gravitationally coupled tensor fields, Nuovo Cim.A 3 (1971) 709 [INSPIRE].
[27] C. Aragone and S. Deser, Consistency Problems of Spin-2 Gravity Coupling, Nuovo Cim.B 57 (1980) 33 [INSPIRE].
[28] Hassan, SF; Rosen, RA, Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity, JHEP, 04, 123, (2012) · Zbl 1348.83065 · doi:10.1007/JHEP04(2012)123
[29] Hassan, SF; Rosen, RA; Schmidt-May, A., Ghost-free Massive Gravity with a General Reference Metric, JHEP, 02, 026, (2012) · Zbl 1309.83084 · doi:10.1007/JHEP02(2012)026
[30] M. Mirbabayi, A Proof Of Ghost Freedom In de Rham-Gabadadze-Tolley Massive Gravity, Phys. Rev.D 86 (2012) 084006 [arXiv:1112.1435] [INSPIRE].
[31] N. Arkani-Hamed, A.G. Cohen and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett.B 513 (2001) 232 [hep-ph/0105239] [INSPIRE]. · Zbl 0969.81657
[32] Arkani-Hamed, N.; Georgi, H.; Schwartz, MD, Effective field theory for massive gravitons and gravity in theory space, Annals Phys., 305, 96, (2003) · Zbl 1022.81035 · doi:10.1016/S0003-4916(03)00068-X
[33] M.D. Schwartz, Constructing gravitational dimensions, Phys. Rev.D 68 (2003) 024029 [hep-th/0303114] [INSPIRE].
[34] N. Arkani-Hamed and M.D. Schwartz, Discrete gravitational dimensions, Phys. Rev.D 69 (2004) 104001 [hep-th/0302110] [INSPIRE]. · Zbl 1405.83011
[35] A.H. Chamseddine and H. Nicolai, Coupling the SO(2) Supergravity Through Dimensional Reduction, Phys. Lett.B 96 (1980) 89.
[36] Dolan, L.; Duff, MJ, Kac-Moody Symmetries of Kaluza-Klein Theories, Phys. Rev. Lett., 52, 14, (1984) · doi:10.1103/PhysRevLett.52.14
[37] L. Dolan, Symmetries of Massive Fields in Kaluza-Klein Supergravity, Phys. Rev.D 30 (1984) 2474 [INSPIRE].
[38] C. Deffayet and J. Mourad, Multigravity from a discrete extra dimension, Phys. Lett.B 589 (2004) 48 [hep-th/0311124] [INSPIRE]. · Zbl 1246.83177
[39] Deffayet, C.; Mourad, J., Some properties of multigravity theories and discretized brane worlds, Int. J. Theor. Phys., 43, 855, (2004) · Zbl 1064.83547 · doi:10.1023/B:IJTP.0000048176.15115.f3
[40] Deffayet, C.; Mourad, J., Deconstruction of gravity, Int. J. Theor. Phys., 44, 1743, (2005) · Zbl 1119.83343 · doi:10.1007/s10773-005-8892-0
[41] C. de Rham, A. Matas and A.J. Tolley, Deconstructing Dimensions and Massive Gravity, Class. Quant. Grav.31 (2014) 025004 [arXiv:1308.4136] [INSPIRE]. · Zbl 1292.83050
[42] Hinterbichler, K.; Rosen, RA, Interacting Spin-2 Fields, JHEP, 07, 047, (2012) · Zbl 1397.83153 · doi:10.1007/JHEP07(2012)047
[43] Deffayet, C.; Mourad, J.; Zahariade, G., A note on ‘symmetric’ vielbeins in bimetric, massive, perturbative and non perturbative gravities, JHEP, 03, 086, (2013) · Zbl 1342.83067 · doi:10.1007/JHEP03(2013)086
[44] S. Deser and P. van Nieuwenhuizen, Nonrenormalizability of the Quantized Dirac-Einstein System, Phys. Rev.D 10 (1974) 411 [INSPIRE].
[45] Ondo, NA; Tolley, AJ, Complete Decoupling Limit of Ghost-free Massive Gravity, JHEP, 11, 059, (2013) · Zbl 1342.83223 · doi:10.1007/JHEP11(2013)059
[46] S.F. Hassan, A. Schmidt-May and M. von Strauss, Metric Formulation of Ghost-Free Multivielbein Theory, arXiv:1204.5202 [INSPIRE].
[47] F. Quevedo, S. Krippendorf and O. Schlotterer, Cambridge Lectures on Supersymmetry and Extra Dimensions, arXiv:1011.1491 [INSPIRE].
[48] Y. Tanii, Introduction to supergravities in diverse dimensions, in YITP Workshop on Supersymmetry, Kyoto, Japan, March 27-30, 1996, (1998) [hep-th/9802138] [INSPIRE].
[49] B. de Wit, Supergravity, in Unity from duality: Gravity, gauge theory and strings. Proceedings, NATO Advanced Study Institute, Euro Summer School, 76th session, Les Houches, France, July 30-August 31, 2001, pp. 1-135 (2002) [hep-th/0212245] [INSPIRE].
[50] Gupta, SN, Gravitation and Electromagnetism, Phys. Rev., 96, 1683, (1954) · Zbl 0056.44103 · doi:10.1103/PhysRev.96.1683
[51] R. Feynman, F. Morinigo, W. Wagner and B. Hatfield, Feynman lectures on gravitation, Addison-Wesley (1996) [INSPIRE].
[52] Weinberg, S., Photons and gravitons in perturbation theory: Derivation of Maxwell’s and Einstein’s equations, Phys. Rev., 138, b988, (1965) · doi:10.1103/PhysRev.138.B988
[53] S. Deser, Self-interaction and gauge invariance, Gen. Rel. Grav.1 (1970) 9 [gr-qc/0411023] [INSPIRE].
[54] Boulware, DG; Deser, S., Classical General Relativity Derived from Quantum Gravity, Annals Phys., 89, 193, (1975) · doi:10.1016/0003-4916(75)90302-4
[55] N. Kiriushcheva and S.V. Kuzmin, The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity in any dimension: The Progress Report, in CAIMS * SCMAI 2009: 30th anniversary of the Canadian Applied and Industrial Mathematics Society, London, Ontario, Canada, June 10-14, 2009, (2009) [arXiv:0907.1553] [INSPIRE].
[56] Kiriushcheva, N.; Kuzmin, SV, Darboux coordinates for the Hamiltonian of first order Einstein-Cartan gravity, Int. J. Theor. Phys., 49, 2859, (2010) · Zbl 1205.83057 · doi:10.1007/s10773-010-0479-y
[57] D.Z. Freedman, P. van Nieuwenhuizen and S. Ferrara, Progress Toward a Theory of Supergravity, Phys. Rev.D 13 (1976) 3214 [INSPIRE].
[58] S. Deser and B. Zumino, Consistent Supergravity, Phys. Lett.B 62 (1976) 335 [INSPIRE].
[59] M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S Matrix, Phys. Rev.D 15 (1977) 996 [INSPIRE].
[60] G. Gabadadze, K. Hinterbichler, D. Pirtskhalava and Y. Shang, Potential for general relativity and its geometry, Phys. Rev.D 88 (2013) 084003 [arXiv:1307.2245] [INSPIRE].
[61] Gregoire, T.; Schwartz, MD; Shadmi, Y., Massive supergravity and deconstruction, JHEP, 07, 029, (2004) · doi:10.1088/1126-6708/2004/07/029
[62] S. Nojiri and S.D. Odintsov, Multisupergravity from latticized extra dimension, Phys. Lett.B 590 (2004) 295 [hep-th/0403162] [INSPIRE]. · Zbl 1246.81290
[63] N. Craig and H.K. Lou, Scherk-Schwarz Supersymmetry Breaking in 4D, JHEP12 (2014) 184 [arXiv:1406.4880] [INSPIRE]. · Zbl 1333.81394
[64] Rham, C.; Matas, A.; Ondo, N.; Tolley, AJ, Interactions of Charged Spin-2 Fields, Class. Quant. Grav., 32, 175008, (2015) · Zbl 1327.83205 · doi:10.1088/0264-9381/32/17/175008
[65] E. Cremmer, Supergravities in 5 Dimensions, (1980) [INSPIRE].
[66] M. Günaydin, G. Sierra and P.K. Townsend, The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys.B 242 (1984) 244 [INSPIRE].
[67] D’Auria, R.; Maina, E.; Regge, T.; Fré, P., Geometrical First Order Supergravity in Five Space-time Dimensions, Annals Phys., 135, 237, (1981) · doi:10.1016/0003-4916(81)90155-X
[68] J. Khoury, J.-L. Lehners and B.A. Ovrut, Supersymmetric Galileons, Phys. Rev.D 84 (2011) 043521 [arXiv:1103.0003] [INSPIRE].
[69] Farakos, F.; Germani, C.; Kehagias, A., On ghost-free supersymmetric galileons, JHEP, 11, 045, (2013) · Zbl 1342.83471 · doi:10.1007/JHEP11(2013)045
[70] M. Srednicki, Quantum field theory, Cambridge University Press (2007) [INSPIRE]. · Zbl 1113.81002
[71] D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press (2012) [INSPIRE]. · Zbl 1245.83001
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