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Off-shell Hodge dualities in linearised gravity and \(E_{11}\). (English) Zbl 1397.81137

Summary: In a spacetime of dimension \(n\), the dual graviton is characterised by a Young diagram with two columns, the first of length \(n-3\) and the second of length one. In this paper we perform the off-shell dualisation relating the dual graviton to the double-dual graviton, displaying the precise off-shell field content and gauge invariances. We then show that one can further perform infinitely many off-shell dualities, reformulating linearised gravity in an infinite number of equivalent actions. The actions require supplementary mixed-symmetry fields which are contained within the generalised Kac-Moody algebra \(E_{11}\) and are associated with null and imaginary roots.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
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[1] West, PC, E_{11} and M-theory, Class. Quant. Grav., 18, 4443, (2001) · Zbl 0992.83079
[2] Damour, T.; Henneaux, M., E_{10}, BE_{10} and arithmetical chaos in superstring cosmology, Phys. Rev. Lett., 86, 4749, (2001)
[3] Damour, T.; Henneaux, M.; Nicolai, H., Cosmological billiards, Class. Quant. Grav., 20, r145, (2003) · Zbl 1138.83306
[4] Julia, B., Group disintegrations, Conf. Proc., C8006162, 331, (1980)
[5] B. Julia, Dualities in the classical supergravity limits: Dualizations, dualities and a detour via (4\(k\) + 2)-dimensions, in the proceedings of the Cargese NATO ASI: Strings, branes and dualities, May 26-June 14, Cargese, France(1997), hep-th/9805083 [INSPIRE].
[6] Boulanger, N.; Cnockaert, S.; Henneaux, M., A note on spin s duality, JHEP, 06, 060, (2003)
[7] Curtright, T., Generalized gauge fields, Phys. Lett., B 165, 304, (1985)
[8] Aulakh, C.; Koh, I.; Ouvry, S., Higher spin fields with mixed symmetry, Phys. Lett., B 173, 284, (1986)
[9] Fierz, M.; Pauli, W., On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond., A 173, 211, (1939) · JFM 65.1532.01
[10] Curtright, TL; Freund, PG, Massive dual fields, Nucl. Phys., B 172, 413, (1980)
[11] Nieto, J., S duality for linearized gravity, Phys. Lett., A 262, 274, (1999) · Zbl 0937.83007
[12] Casini, H.; Montemayor, R.; Urrutia, LF, Dual theories for mixed symmetry fields. spin two case: (1, 1) versus (2, 1) Young symmetry type fields, Phys. Lett., B 507, 336, (2001) · Zbl 0977.81159
[13] Hull, C., Duality in gravity and higher spin gauge fields, JHEP, 09, 027, (2001)
[14] Bekaert, X.; Boulanger, N., Tensor gauge fields in arbitrary representations of GL(D, R): duality and Poincaré lemma, Commun. Math. Phys., 245, 27, (2004) · Zbl 1074.81052
[15] Casini, H.; Montemayor, R.; Urrutia, LF, duality for symmetric second rank tensors. 2. the linearized gravitational field, Phys. Rev., D 68, 065011, (2003)
[16] Ajith, K.; Harikumar, E.; Sivakumar, M., Dual linearised gravity in arbitrary dimensions from buscher’s construction, Class. Quant. Grav., 22, 5385, (2005) · Zbl 1088.83013
[17] Zinoviev, Y., On dual formulations of massive tensor fields, JHEP, 10, 075, (2005)
[18] Y. Zinoviev, On dual formulation of gravity, hep-th/0504210 [INSPIRE].
[19] Henneaux, M.; Teitelboim, C., Duality in linearized gravity, Phys. Rev., D 71, 024018, (2005)
[20] Julia, B.; Levie, J.; Ray, S., Gravitational duality near de Sitter space, JHEP, 11, 025, (2005)
[21] Leigh, RG; Petkou, AC, Gravitational duality transformations on (A)ds(4), JHEP, 11, 079, (2007) · Zbl 1245.83068
[22] Barnich, G.; Troessaert, C., Manifest spin 2 duality with electric and magnetic sources, JHEP, 01, 030, (2009) · Zbl 1243.81210
[23] Deser, S.; Seminara, D., Free spin 2 duality invariance cannot be extended to GR, Phys. Rev., D 71, 081502, (2005)
[24] Boulanger, N.; Hohm, O., Non-linear parent action and dual gravity, Phys. Rev., D 78, 064027, (2008)
[25] West, PC, Very extended E_{8} and A_{8} at low levels, gravity and supergravity, Class. Quant. Grav., 20, 2393, (2003) · Zbl 1025.83030
[26] Hull, C., Symmetries and compactifications of (4, 0) conformal gravity, JHEP, 12, 007, (2000) · Zbl 0990.81725
[27] Hull, C., Strongly coupled gravity and duality, Nucl. Phys., B 583, 237, (2000) · Zbl 0983.83051
[28] Riccioni, F.; West, PC, Dual fields and E_{11}, Phys. Lett., B 645, 286, (2007) · Zbl 1256.83032
[29] Chiodaroli, M.; Günaydin, M.; Roiban, R., Superconformal symmetry and maximal supergravity in various dimensions, JHEP, 03, 093, (2012) · Zbl 1309.81241
[30] Englert, F.; Houart, L.; Kleinschmidt, A.; Nicolai, H.; Tabti, N., An E_{9} multiplet of BPS states, JHEP, 05, 065, (2007)
[31] Geroch, RP, A method for generating solutions of einstein’s equations, J. Math. Phys., 12, 918, (1971) · Zbl 0214.49002
[32] Geroch, RP, A method for generating new solutions of einstein’s equation 2, J. Math. Phys., 13, 394, (1972) · Zbl 0241.53038
[33] Breitenlohner, P.; Maison, D., On the Geroch group, Annales Poincaré Phys. Theor., 46, 215, (1987) · Zbl 0614.53039
[34] Damour, T.; Henneaux, M.; Nicolai, H., E_{10} and a ’small tension expansion’ of M-theory, Phys. Rev. Lett., 89, 221601, (2002) · Zbl 1267.83103
[35] Bergshoeff, EA; Roo, M.; Hohm, O., Can dual gravity be reconciled with E11?, Phys. Lett., B 675, 371, (2009)
[36] Bergshoeff, EA; Roo, M.; Kerstan, SF; Kleinschmidt, A.; Riccioni, F., Dual gravity and matter, Gen. Rel. Grav., 41, 39, (2009) · Zbl 1162.83329
[37] Bekaert, X.; Boulanger, N.; Henneaux, M., Consistent deformations of dual formulations of linearized gravity: a no go result, Phys. Rev., D 67, 044010, (2003)
[38] Boulanger, N.; Cnockaert, S., Consistent deformations of [p, p] type gauge field theories, JHEP, 03, 031, (2004)
[39] Bekaert, X.; Boulanger, N.; Cnockaert, S., No self-interaction for two-column massless fields, J. Math. Phys., 46, 012303, (2005) · Zbl 1076.81039
[40] Y.M. Zinoviev, First order formalism for mixed symmetry tensor fields, hep-th/0304067 [INSPIRE].
[41] Skvortsov, E., Mixed-symmetry massless fields in Minkowski space unfolded, JHEP, 07, 004, (2008)
[42] Skvortsov, E., Frame-like actions for massless mixed-symmetry fields in Minkowski space, Nucl. Phys., B 808, 569, (2009) · Zbl 1192.81224
[43] Skvortsov, E.; Zinoviev, Y., Frame-like actions for massless mixed-symmetry fields in Minkowski space. fermions, Nucl. Phys., B 843, 559, (2011) · Zbl 1207.81078
[44] Fradkin, E.; Tseytlin, AA, Quantum equivalence of dual field theories, Annals Phys., 162, 31, (1985)
[45] H. Weyl, Electron and gravitation 1 (in German), Surv. High Energ. Phys.5 (1986) 261 [Z. Phys.56 (1929) 330] [INSPIRE].
[46] Riccioni, F.; West, PC, The E_{11} origin of all maximal supergravities, JHEP, 07, 063, (2007)
[47] Riccioni, F.; Steele, D.; West, P., The E_{11} origin of all maximal supergravities: the hierarchy of field-strengths, JHEP, 09, 095, (2009)
[48] Riccioni, F.; Proeyen, A.; West, PC, Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries, JHEP, 05, 079, (2008)
[49] Strathdee, J., Extended poincare supersymmetry, Int. J. Mod. Phys., A 2, 273, (1987) · Zbl 1165.81334
[50] Englert, F.; Houart, L.; Taormina, A.; West, PC, The symmetry of M theories, JHEP, 09, 020, (2003)
[51] Siegel, W., All free conformal representations in all dimensions, Int. J. Mod. Phys., A 4, 2015, (1989)
[52] Bekaert, X.; Boulanger, N., Tensor gauge fields in arbitrary representations of GL(D, R). II. quadratic actions, Commun. Math. Phys., 271, 723, (2007) · Zbl 1122.81061
[53] Cook, PP, Exotic E_{11} branes as composite gravitational solutions, Class. Quant. Grav., 26, 235023, (2009) · Zbl 1181.83042
[54] N. Boulanger and D. Ponomarev, Frame-like off-shell dualisation for mixed-symmetry gauge fields, arXiv:1206.2052 [INSPIRE]. · Zbl 1268.81111
[55] Henneaux, M.; Kleinschmidt, A.; Nicolai, H., Real forms of extended Kac-Moody symmetries and higher spin gauge theories, Gen. Rel. Grav., 44, 1787, (2012) · Zbl 1246.83221
[56] Bekaert, X.; Boulanger, N., On geometric equations and duality for free higher spins, Phys. Lett., B 561, 183, (2003) · Zbl 1094.81523
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