Abstract
We discuss the connection between Weyl2 supergravity and superstrings and further discuss holography between 4-dimensional, \( \mathcal{N} \) = 4 superconformal Weyl2 supergravity and \( \mathcal{N} \) = 8, higher spin-four theory on AdS5. The Weyl2 plus Einstein supergravity theory is a special kind of a bimetric gravity theory and consists of a massless graviton multiplet plus an additional massive spin-two supermultiplet. Here, we argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the \( \mathcal{N} \) = 4 super Yang-Mills gauge fields, they are localized on the world volume of D3-branes. The ghost structure of the Weyl action should be considered as an artifact of the truncation of the infinitely many higher derivative terms underlying the massive spin 2 action. In field theory, \( \mathcal{N} \) = 4 Weyl2 supergravity exhibits superconformal invariance in the limit of vanishing Planck mass. In string theory the additional spin-two fields become massless in the tensionless limit. Therefore low string scale scenarios with large extra dimensions provide (almost) superconformal field theories with almost massless open string spin-two fields. The full \( \mathcal{N} \) = 4 scalar potential including the Yang-Mills matter multiplets is presented and the supersymmetric vacua of Einstein Supergravity are shown, as expected, to be vacua of massive Weyl supergravity. Other vacua are expected to exist which are not vacua of Einstein supergravity. Finally, we identify certain spin-four operators on the 4-dimensional boundary theory that could be the holographic duals of spin-four fields in the bulk.
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References
K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
K.S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
D.G. Boulware, G.T. Horowitz and A. Strominger, Zero energy theorem for scale invariant gravity, Phys. Rev. Lett. 50 (1983) 1726 [INSPIRE].
F. David and A. Strominger, On the calculability of Newton’s constant and the renormalizability of scale invariant quantum gravity, Phys. Lett. 143B (1984) 125 [INSPIRE].
G.T. Horowitz, Quantum cosmology with a positive definite action, Phys. Rev. D 31 (1985) 1169 [INSPIRE].
S. Deser and B. Tekin, Shortcuts to high symmetry solutions in gravitational theories, Class. Quant. Grav. 20 (2003) 4877 [gr-qc/0306114] [INSPIRE].
S. Deser and B. Tekin, New energy definition for higher curvature gravities, Phys. Rev. D 75 (2007) 084032 [gr-qc/0701140] [INSPIRE].
G. ’t Hooft, A class of elementary particle models without any adjustable real parameters, Found. Phys. 41 (2011) 1829 [arXiv:1104.4543] [INSPIRE].
J. Maldacena, Einstein gravity from conformal gravity, arXiv:1105.5632 [INSPIRE].
H. Lü, C.N. Pope, E. Sezgin and L. Wulff, Critical and non-critical Einstein-Weyl supergravity, JHEP 10 (2011) 131 [arXiv:1107.2480] [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, 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, 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, E. Joung and A. Waldron, Gravitational- and self- coupling of partially massless spin 2, Phys. Rev. D 86 (2012) 104004 [arXiv:1301.4181] [INSPIRE].
F. Del Monte, D. Francia and P.A. Grassi, Multimetric supergravities, JHEP 09 (2016) 064 [arXiv:1605.06793] [INSPIRE].
S. Ferrara, A. Kehagias and D. Lüst, Aspects of Weyl supergravity, JHEP 08 (2018) 197 [arXiv:1806.10016] [INSPIRE].
S. Ferrara, M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Gauging the graded conformal group with unitary internal symmetries, Nucl. Phys. B 129 (1977) 125 [INSPIRE].
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Superconformal unified field theory, Phys. Rev. Lett. 39 (1977) 1109 [INSPIRE].
M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of conformal supergravity, Phys. Rev. D 17 (1978) 3179 [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).
E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept. 119 (1985) 233 [INSPIRE].
B. de Wit and S. Ferrara, On higher order invariants in extended supergravity, Phys. Lett. B 81 (1979) 317.
D. Lüst, S. Stieberger and T.R. Taylor, The LHC string hunter’s companion, Nucl. Phys. B 808 (2009) 1 [arXiv:0807.3333] [INSPIRE].
L. Álvarez-Gaumé et al., Aspects of quadratic gravity, Fortsch. Phys. 64 (2016) 176 [arXiv:1505.07657] [INSPIRE].
A. Salvio, Quadratic gravity, Front. in Phys. 6 (2018) 77 [arXiv:1804.09944] [INSPIRE].
P.K. Townsend and P. van Nieuwenhuizen, Simplifications of conformal supergravity, Phys. Rev. D 19 (1979) 3166 [INSPIRE].
S. Cecotti, S. Ferrara, M. Porrati and S. Sabharwal, New minimal higher derivative supergravity coupled to matter, Nucl. Phys. B 306 (1988) 160 [INSPIRE].
S. Ferrara and M. Villasante, Curvatures, Gauss-Bonnet and Chern-Simons multiplets in old minimal N = 1 supergravity, J. Math. Phys. 30 (1989) 104 [INSPIRE].
F. Farakos, S. Ferrara, A. Kehagias and D. Lüst, Non-linear realizations and higher curvature supergravity, Fortsch. Phys. 65 (2017) 1700073 [arXiv:1707.06991] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
B. Gording and A. Schmidt-May, Ghost-free infinite derivative gravity, JHEP 09 (2018) 044 [Erratum ibid. 1810 (2018) 115] [arXiv:1807.05011] [INSPIRE].
S. Ferrara and B. Zumino, Structure of conformal supergravity, Nucl. Phys. B 134 (1978) 301 [INSPIRE].
S. Ferrara and B. Zumino, Transformation properties of the supercurrent, Nucl. Phys. B 87 (1975) 207 [INSPIRE].
S. Ferrara, M.T. Grisaru and P. van Nieuwenhuizen, Poincaré and conformal supergravity models with closed algebras, Nucl. Phys. B 138 (1978) 430 [INSPIRE].
R.J. Riegert, The particle content of linearized conformal gravity, Phys. Lett. A 105 (1984) 110 [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].
E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
J.P. Derendinger and S. Ferrara, N = 1 and N = 2 supergravities coupled to matter: superhiggs effect and geometrical structure, in Supersymmetry and Supergravity 1984, B. de Wit et al. eds., World Scientific, Singapore (1984).
M. de Roo, Matter coupling in N = 4 supergravity, Nucl. Phys. B 255 (1985) 515 [INSPIRE].
M. de Roo, Gauged N = 4 matter couplings, Phys. Lett. B 156 (1985) 331.
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].
N. Berkovits and E. Witten, Conformal supergravity in twistor-string theory, JHEP 08 (2004) 009 [hep-th/0406051] [INSPIRE].
S. Ferrara, C.A. Savoy and B. Zumino, General massive multiplets in extended supersymmetry, Phys. Lett. B 100 (1981) 393.
H. Johansson, G. Mogull and F. Teng, Unraveling conformal gravity amplitudes, JHEP 09 (2018) 080 [arXiv:1806.05124] [INSPIRE].
W.-Z. Feng et al., Direct production of lightest Regge resonances, Nucl. Phys. B 843 (2011) 570 [arXiv:1007.5254] [INSPIRE].
R. Blumenhagen, D. Lüst and S. Theisen, Basic concepts of string theory, Springer, Germany (2012).
S. Ferrara and D. Lüst, Spin-four \( \mathcal{N} \) = 7 W-supergravity: S-fold and double copy construction, JHEP 07 (2018) 114 [arXiv:1805.10022] [INSPIRE].
H. Liu and A.A. Tseytlin, D = 4 superYang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity, Nucl. Phys. B 533 (1998) 88 [hep-th/9804083] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
V. Balasubramanian, E.G. Gimon, D. Minic and J. Rahmfeld, Four-dimensional conformal supergravity from AdS space, Phys. Rev. D 63 (2001) 104009 [hep-th/0007211] [INSPIRE].
M. Abou-Zeid, Actions for curved branes, hep-th/0001127 [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].
C. Bachas and I. Lavdas, Massive Anti-de Sitter gravity from string theory, JHEP 11 (2018) 003 [arXiv:1807.00591] [INSPIRE].
L. Bel, Sur la radiation gravitationelle, C. R. Math. Acad. Sci. Paris 247 (1958) 1094.
L. Bel, Introduction d’un tenseur du quartieme order, C. R. Math. Acad. Sci. Paris 248 (1959) 1297.
I. Robinson, unpublished King’s College lectures, London, U.K. (1958).
I. Robinson, On the Bel-Robinson tensor, Class. Quant. Grav. 14 (1997) 4331
S. Deser and A. Waldron, Arbitrary spin representations in de Sitter from dS/CFT with applications to dS supergravity, Nucl. Phys. B 662 (2003) 379 [hep-th/0301068] [INSPIRE].
R.R. Metsaev, Massive totally symmetric fields in AdS(d), Phys. Lett. B 590 (2004) 95 [hep-th/0312297] [INSPIRE].
S. Weinberg, Effective field theory for inflation, Phys. Rev. D 77 (2008) 123541 [arXiv:0804.4291] [INSPIRE].
S. Ferrara, R. Kallosh and A. Van Proeyen, Conjecture on hidden superconformal symmetry of N = 4 supergravity, Phys. Rev. D 87 (2013) 025004 [arXiv:1209.0418] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, One loop β-function in conformal supergravities, Nucl. Phys. B 203 (1982) 157 [INSPIRE].
D.M. Capper and M.J. Duff, Conformal anomalies and the renormalizability problem in quantum gravity, Phys. Lett. A 53 (1975) 361 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Conformal anomaly in Weyl theory and anomaly free superconformal theories, Phys. Lett. B 134 (1984) 187.
A.A. Tseytlin, On divergences in non-minimal N = 4 conformal supergravity, J. Phys. A 50 (2017) 48LT01 [arXiv:1708.08727] [INSPIRE].
H. Römer and P. van Nieuwenhuizen, Axial anomalies in N = 4 conformal supergravity, Phys. Lett. B 162 (1985) 290.
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Ferrara, S., Kehagias, A. & Lüst, D. Bimetric, conformal supergravity and its superstring embedding. J. High Energ. Phys. 2019, 100 (2019). https://doi.org/10.1007/JHEP05(2019)100
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DOI: https://doi.org/10.1007/JHEP05(2019)100