Abstract
Making use of integral forms and superfield techniques we propose supersymmetric extensions of the multimetric gravity Lagrangians in dimensions one, two, three and four. The supersymmetric interaction potential covariantly deforms the bosonic one, producing in particular suitable super-symmetric polynomials generated by the Berezinian. As an additional application of our formalism we construct supersymmetric multi-Maxwell theories in dimensions three and four.
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M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [INSPIRE].
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
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].
S.F. Hassan, R.A. Rosen and A. Schmidt-May, Ghost-free massive gravity with a general reference metric, JHEP 02 (2012) 026 [arXiv:1109.3230] [INSPIRE].
S.F. Hassan and R.A. Rosen, Bimetric gravity from ghost-free massive gravity, JHEP 02 (2012) 126 [arXiv:1109.3515] [INSPIRE].
S.F. Hassan and R.A. Rosen, Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity, JHEP 04 (2012) 123 [arXiv:1111.2070] [INSPIRE].
K. Hinterbichler and R.A. Rosen, Interacting spin-2 fields, JHEP 07 (2012) 047 [arXiv:1203.5783] [INSPIRE].
S. Groot Nibbelink, M. Peloso and M. Sexton, Nonlinear properties of vielbein massive gravity, Eur. Phys. J. C 51 (2007) 741 [hep-th/0610169] [INSPIRE].
D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
C. de Rham, Massive gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
A. Schmidt-May and M. von Strauss, Recent developments in bimetric theory, J. Phys. A 49 (2016) 183001 [arXiv:1512.00021] [INSPIRE].
S. Deser, M. Sandora and A. Waldron, No consistent bimetric gravity?, Phys. Rev. D 88 (2013) 081501 [arXiv:1306.0647] [INSPIRE].
R. Catenacci, M. Debernardi, P.A. Grassi and D. Matessi, Balanced superprojective varieties, J. Geom. Phys. 59 (2009) 1363 [arXiv:0707.4246] [INSPIRE].
R. Catenacci, M. Debernardi, P.A. Grassi and D. Matessi, Čech and de Rham cohomology of integral forms, J. Geom. Phys. 62 (2012) 890 [arXiv:1003.2506] [INSPIRE].
L. Castellani, R. Catenacci and P.A. Grassi, The geometry of supermanifolds and new supersymmetric actions, Nucl. Phys. B 899 (2015) 112 [arXiv:1503.07886] [INSPIRE].
A.H. Chamseddine, Massive supergravity from spontaneously breaking orthosymplectic gauge symmetry, Annals Phys. 113 (1978) 219 [INSPIRE].
S. Deser and J.H. Kay, Topologically massive supergravity, Phys. Lett. B 120 (1983) 97 [INSPIRE].
S. Deser, Cosmological topological supergravity, in Quantum theory of gravity, S.M. Christensen ed. (1982), pp. 374-381 [INSPIRE].
P.S. Howe, N.D. Lambert and P.C. West, A new massive type IIA supergravity from compactification, Phys. Lett. B 416 (1998) 303 [hep-th/9707139] [INSPIRE].
N. Kaloper and R.C. Myers, The odd story of massive supergravity, JHEP 05 (1999) 010 [hep-th/9901045] [INSPIRE].
I. Schnakenburg and P.C. West, Massive IIA supergravity as a nonlinear realization, Phys. Lett. B 540 (2002) 137 [hep-th/0204207] [INSPIRE].
G.W. Gibbons, C.N. Pope and E. Sezgin, The general supersymmetric solution of topologically massive supergravity, Class. Quant. Grav. 25 (2008) 205005 [arXiv:0807.2613] [INSPIRE].
R. Andringa et al., Massive 3D supergravity, Class. Quant. Grav. 27 (2010) 025010 [arXiv:0907.4658] [INSPIRE].
E.A. Bergshoeff, O. Hohm, J. Rosseel, E. Sezgin and P.K. Townsend, More on massive 3D supergravity, Class. Quant. Grav. 28 (2011) 015002 [arXiv:1005.3952] [INSPIRE].
O. Malaeb, Supersymmetrizing massive gravity, Phys. Rev. D 88 (2013) 025002 [arXiv:1303.3580] [INSPIRE].
S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Higher derivative couplings and massive supergravity in three dimensions, JHEP 09 (2015) 081 [arXiv:1506.09063] [INSPIRE].
C. de Rham and A.J. Tolley, Vielbein to the rescue? Breaking the symmetric vielbein condition in massive gravity and multigravity, Phys. Rev. D 92 (2015) 024024 [arXiv:1505.01450] [INSPIRE].
C. Deffayet, J. Mourad and G. Zahariade, A note on ‘symmetric’ vielbeins in bimetric, massive, perturbative and non perturbative gravities, JHEP 03 (2013) 086 [arXiv:1208.4493] [INSPIRE].
H.R. Afshar, E.A. Bergshoeff and W. Merbis, Interacting spin-2 fields in three dimensions, JHEP 01 (2015) 040 [arXiv:1410.6164] [INSPIRE].
J.H.C. Scargill, J. Noller and P.G. Ferreira, Cycles of interactions in multi-gravity theories, JHEP 12 (2014) 160 [arXiv:1410.7774] [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
P.C. West, Introduction to supersymmetry and supergravity, World Scientific, Singapore (1990) [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992) [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity: a walk through superspace, IOP, Bristol U.K. (1995) [INSPIRE].
F. Ruiz Ruiz and P. van Nieuwenhuizen, Lectures on supersymmetry and supergravity in (2+1)-dimensions and regularization of supersymmetric gauge theories, in Recent developments in gravitation and mathematical physics. Proceedings of the 2nd Mexican School, Tlaxcala Mexico, 1-7 Dec 1996 [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, U. Lindström, M. Roček, I. Sachs and G. Tartaglino-Mazzucchelli, Three-dimensional \( \mathcal{N} \) = 2 supergravity theories: from superspace to components, Phys. Rev. D 89 (2014) 085028 [arXiv:1312.4267] [INSPIRE].
M. Becker et al., M-theory on Spin(7) manifolds, fluxes and 3D, \( \mathcal{N} \) = 1 supergravity, Nucl. Phys. B 683 (2004) 67 [hep-th/0312040] [INSPIRE].
F.F. Voronov and A.V. Zorich, Integral transformations of pseudodifferential forms, Usp. Mat. Nauk 41 (1986) 167.
F.F. Voronov and A.V. Zorich, Complex of forms on a supermanifold, Funktsional. Anal. Prilozhen. 20 (1986) 58.
F.F. Voronov and A.V. Zorich, Theory of bordisms and homotopy properties of supermanifolds, Funktsional. Anal. Prilozhen. 21 (1987) 77.
F.F. Voronov and A.V. Zorich, Cohomology of supermanifolds, and integral geometry, Soviet Math. Dokl. 37 (1988) 96.
F.F. Voronov and A.V. Zorich, Integration on vector bundles, Funct. Anal. Appl. 22 (1988) 94.
E. Witten, Notes on supermanifolds and integration, arXiv:1209.2199 [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
A. Belopolsky, De Rham cohomology of the supermanifolds and superstring BRST cohomology, Phys. Lett. B 403 (1997) 47 [hep-th/9609220] [INSPIRE].
A. Belopolsky, Picture changing operators in supergeometry and superstring theory, hep-th/9706033 [INSPIRE].
P.A. Grassi and G. Policastro, Super-Chern-Simons theory as superstring theory, hep-th/0412272 [INSPIRE].
E. Witten, Superstring perturbation theory revisited, arXiv:1209.5461 [INSPIRE].
D.P. Sorokin, Superbranes and superembeddings, Phys. Rept. 329 (2000) 1 [hep-th/9906142] [INSPIRE].
P.S. Howe, Super Weyl transformations in two-dimensions, J. Phys. A 12 (1979) 393 [INSPIRE].
M.F. Ertl, Supergravity in two space-time dimensions, hep-th/0102140 [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].
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Del Monte, F., Francia, D. & Grassi, P.A. Multimetric supergravities. J. High Energ. Phys. 2016, 64 (2016). https://doi.org/10.1007/JHEP09(2016)064
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DOI: https://doi.org/10.1007/JHEP09(2016)064