Abstract
The most general class of 4D \( \mathcal{N} \) = 4 conformal supergravity actions depends on a holomorphic function of the scalar fields that parametrize an SU(1, 1)/U(1) coset space. The bosonic sector of these actions was presented in a letter [1]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new \( \mathcal{N} \) = 4 density formula, which permits a direct but involved construction. This density formula also recovers the on-shell action for vector multiplets coupled to conformal supergravity. Applications of these results in the context of Poincaré supergravity are briefly discussed.
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D. Butter, F. Ciceri, B. de Wit and B. Sahoo, Construction of all N = 4 conformal supergravities, Phys. Rev. Lett.118 (2017) 081602 [arXiv:1609.09083] [INSPIRE].
M. Kaku and P.K. Townsend, Poincaré supergravity as broken superconformal gravity, Phys. Lett.76B (1978) 54 [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of conformal supergravity, Phys. Rev.D 17 (1978) 3179 [INSPIRE].
B. de Wit, J.W. van Holten and A. Van Proeyen, Transformation rules of N = 2 supergravity multiplets, Nucl. Phys.B 167 (1980) 186 [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys.B 182 (1981) 173 [INSPIRE].
J. van Muiden and A. Van Proeyen, The \( \mathcal{N} \) = 3 Weyl multiplet in four dimensions, JHEP01 (2019) 167 [arXiv:1702.06442] [INSPIRE].
S. Hegde and B. Sahoo, Comment on “The N = 3 Weyl multiplet in four dimensions”, Phys. Lett.B 791 (2019) 92 [arXiv:1810.05089] [INSPIRE].
D. Butter, S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Conformal supergravity in three dimensions: Off-shell actions, JHEP10 (2013) 073 [arXiv:1306.1205] [INSPIRE].
M. Nishimura and Y. Tanii, N = 6 conformal supergravity in three dimensions, JHEP10 (2013) 123 [arXiv:1308.3960] [INSPIRE].
S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, N = 6 superconformal gravity in three dimensions from superspace, JHEP01 (2014) 121 [arXiv:1308.5552] [INSPIRE].
E.A. Bergshoeff, O. Hohm, J. Rosseel and P.K. Townsend, On maximal massive 3D supergravity, Class. Quant. Grav.27 (2010) 235012 [arXiv:1007.4075] [INSPIRE].
D. Butter, S.M. Kuzenko, J. Novak and S. Theisen, Invariants for minimal conformal supergravity in six dimensions, JHEP12 (2016) 072 [arXiv:1606.02921] [INSPIRE].
D. Butter, J. Novak and G. Tartaglino-Mazzucchelli, The component structure of conformal supergravity invariants in six dimensions, JHEP05 (2017) 133 [arXiv:1701.08163] [INSPIRE].
I.L. Buchbinder, N.G. Pletnev and A.A. Tseytlin, “Induced” N = 4 conformal supergravity, Phys. Lett.B 717 (2012) 274 [arXiv:1209.0416] [INSPIRE].
F. Ciceri and B. Sahoo, Towards the full N = 4 conformal supergravity action, JHEP01 (2016) 059 [arXiv:1510.04999] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, One loop β-function in conformal supergravities, Nucl. Phys.B 203 (1982) 157 [INSPIRE].
J.A. Harvey and G.W. Moore, Five-brane instantons and R 2couplings in N = 4 string theory, Phys. Rev.D 57 (1998) 2323 [hep-th/9610237] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Asymptotic degeneracy of dyonic N = 4 string states and black hole entropy, JHEP12 (2004) 075 [hep-th/0412287] [INSPIRE].
D.P. Jatkar and A. Sen, Dyon spectrum in CHL models, JHEP04 (2006) 018 [hep-th/0510147] [INSPIRE].
G. Bossard, P.S. Howe and K.S. Stelle, Anomalies and divergences in N = 4 supergravity, Phys. Lett.B 719 (2013) 424 [arXiv:1212.0841] [INSPIRE].
G. Bossard, P.S. Howe and K.S. Stelle, Invariants and divergences in half-maximal supergravity theories, JHEP07 (2013) 117 [arXiv:1304.7753] [INSPIRE].
K. Peeters, Introducing Cadabra: a symbolic computer algebra system for field theory problems, hep-th/0701238 [INSPIRE].
K. Peeters, A field-theory motivated approach to symbolic computer algebra, Comput. Phys. Commun.176 (2007) 550 [cs/0608005] [INSPIRE].
M. de Roo, Matter coupling in N = 4 supergravity, Nucl. Phys.B 255 (1985) 515 [INSPIRE].
M. de Roo and P. Wagemans, Gauge matter coupling in N = 4 supergravity, Nucl. Phys.B 262 (1985) 644 [INSPIRE].
S.J. Gates, Jr., Ectoplasm has no topology: the prelude, in the proceedings of the Supersymmetries and Quantum Symmetries (SQS’97), July 22–26, Dubna, Russia (1997), hep-th/9709104 [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M.E. Knutt-Wehlau and W. Siegel, Component actions from curved superspace: Normal coordinates and ectoplasm, Phys. Lett.B 421 (1998) 203 [hep-th/9711151] [INSPIRE].
R. D’Auria, P. Fré, P.K. Townsend and P. van Nieuwenhuizen, Invariance of Actions, Rheonomy and the New Minimal N = 1 Supergravity in the Group Manifold Approach, Annals Phys.155 (1984) 423 [INSPIRE].
L. Castellani, R. D’Auria and P. Fre, Supergravity and superstrings: a geometric perspective. Volume 2: supergravity, World Scientific, Singapore (1991).
F. Brandt, Supersymmetry algebra cohomology III: primitive elements in four and five dimensions, J. Math. Phys.52 (2011) 052301 [arXiv:1005.2102] [INSPIRE].
M.F. Sohnius, Bianchi identities for supersymmetric gauge theories, Nucl. Phys.B 136 (1978) 461 [INSPIRE].
G.G. Hartwell and P.S. Howe, (N, p, q) harmonic superspace, Int. J. Mod. Phys.A 10 (1995) 3901 [hep-th/9412147] [INSPIRE].
P.S. Howe and G.G. Hartwell, A superspace survey, Class. Quant. Grav.12 (1995) 1823 [INSPIRE].
N. Berkovits, Explaining pure spinor superspace, hep-th/0612021 [INSPIRE].
G. Bossard and H. Nicolai, Counterterms vs. dualities, JHEP08 (2011) 074 [arXiv:1105.1273] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black hole entropy, Phys. Lett.B 451 (1999) 309 [hep-th/9812082] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R 2interactions, JHEP12 (2000) 019 [hep-th/0009234] [INSPIRE].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP09 (2005) 038 [hep-th/0506177] [INSPIRE].
A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav.40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Quantum black holes, localization and the topological string, JHEP06 (2011) 019 [arXiv:1012.0265] [INSPIRE].
S. Murthy and V. Reys, Functional determinants, index theorems and exact quantum black hole entropy, JHEP12 (2015) 028 [arXiv:1504.01400] [INSPIRE].
Z. Bern et al., Ultraviolet properties of N = 4 supergravity at four loops, Phys. Rev. Lett.111 (2013) 231302 [arXiv:1309.2498] [INSPIRE].
J.J.M. Carrasco, R. Kallosh, R. Roiban and A.A. Tseytlin, On the U(1) duality anomaly and the S-matrix of N = 4 supergravity, JHEP07 (2013) 029 [arXiv:1303.6219] [INSPIRE].
Z. Bern, J. Parra-Martinez and R. Roiban, Canceling the U(1) anomaly in the S matrix of N = 4 supergravity, Phys. Rev. Lett.121 (2018) 101604 [arXiv:1712.03928] [INSPIRE].
Z. Bern, D. Kosower and J. Parra-Martinez, Two-loop n-point anomalous amplitudes in N = 4 supergravity, arXiv:1905.05151 [INSPIRE].
D. Butter, N = 1 conformal superspace in four dimensions, Annals Phys.325 (2010) 1026 [arXiv:0906.4399] [INSPIRE].
D. Butter, N = 2 conformal superspace in four dimensions, JHEP10 (2011) 030 [arXiv:1103.5914] [INSPIRE].
P.S. Howe, Supergravity in superspace, Nucl. Phys.B 199 (1982) 309 [INSPIRE].
S.J. Gates Jr., On-shell and conformal N = 4 supergravity in superspace, Nucl. Phys.B 213 (1983) 409 [INSPIRE].
J. Wess and J.A. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).
E. Bergshoeff, E. Sezgin and A. Van Proeyen, (2, 0) tensor multiplets and conformal supergravity in D = 6, Class. Quant. Grav.16 (1999) 3193 [hep-th/9904085] [INSPIRE].
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Butter, D., Ciceri, F. & Sahoo, B. \( \mathcal{N} \) = 4 conformal supergravity: the complete actions. J. High Energ. Phys. 2020, 29 (2020). https://doi.org/10.1007/JHEP01(2020)029
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DOI: https://doi.org/10.1007/JHEP01(2020)029