Bizdadea, C.; Ciobírcă, C. C.; Cioroianu, E. M.; Saliu, S. O.; Săraru, S. C. Interactions of a massless tensor field with the mixed symmetry of the Riemann tensor. No-go results. (English) Zbl 1191.81193 Eur. Phys. J. C, Part. Fields 36, No. 2, 253-270 (2004). Summary: Non-trivial, consistent interactions of a free, massless tensor field \(t_{\mu \nu |\alpha \beta}\) with the mixed symmetry of the Riemann tensor are studied in the following cases: self-couplings, cross-interactions with a Pauli-Fierz field and cross-couplings with purely matter theories. The main results, obtained from BRST cohomological techniques under the assumptions of smoothness, locality, Lorentz covariance and Poincaré invariance of the deformations, combined with the requirement that the interacting Lagrangian is at most second-order derivative, can be synthesized into the following results: no consistent self-couplings exist, but a cosmological-like term; no cross-interactions with the Pauli-Fierz field can be added; no non-trivial consistent cross-couplings with the matter theories such that the matter fields gain gauge transformations are allowed. Cited in 7 Documents MSC: 81T70 Quantization in field theory; cohomological methods 83E99 Unified, higher-dimensional and super field theories PDFBibTeX XMLCite \textit{C. Bizdadea} et al., Eur. Phys. J. C, Part. Fields 36, No. 2, 253--270 (2004; Zbl 1191.81193) Full Text: DOI arXiv References: [1] T. Curtright, Phys. Lett. B 165, 304 (1985); T. Curtright, P.G.O. Freund, Nucl. Phys. B 172, 413 (1980) [2] C.S. Aulakh, I.G. Koh, S. Ouvry, Phys. Lett. B 173, 284 (1986) [3] J.M. Labastida, T.R. Morris, Phys. Lett. B 180, 101 (1986); J.M. Labastida, Nucl. Phys. B 322, 185 (1989) [4] C. Burdik, A. Pashnev, M. Tsulaia, Mod. Phys. Lett. A 16, 731 (2001) · Zbl 1138.81433 [5] Yu.M. Zinoviev, hep-th/0211233 [6] C.M. Hull, JHEP 0109, 027 (2001) [7] X. Bekaert, N. Boulanger, Commun. Math. Phys. 245, 27 (2004) · Zbl 1074.81052 [8] X. Bekaert, N. Boulanger, Class. Quant. Grav. 20, S417 (2003); Phys. Lett. B 561, 183 (2003) [9] H. Casini, R. Montemayor, L.F. Urrutia, hep-th/0304228 [10] N. Boulanger, S. Cnockaert, M. Henneaux, JHEP 0306, 060 (2003) [11] H. Casini, R. Montemayor, L.F. Urrutia, Phys. Lett. B 507, 336 (2001); P. de Medeiros, C. Hull, Commun. Math. Phys. 235, 255 (2003) · Zbl 0977.81159 [12] X. Bekaert, N. Boulanger, M. Henneaux, Phys. Rev. D 67, 044010 (2003) [13] Yu.M. Zinoviev, hep-th/0304067 [14] Yu.M. Zinoviev, hep-th/0306292 [15] A.K. Bengtsson, I. Bengtsson, L. Brink, Nucl. Phys. B 227, 41 (1983) [16] M.A. Vasiliev, Nucl. Phys. B 616, 106 (2001); Erratum B 652, 407 (2003) · Zbl 0988.81071 [17] E. Sezgin, P. Sundell, Nucl. Phys. B 634, 120 (2002) · Zbl 0995.81059 [18] D. Francia, A. Sagnotti, Phys. Lett. B 543, 303 (2002) · Zbl 0997.81072 [19] C. Bizdadea, C.C. Ciobirca, E.M. Cioroianu, I. Negru, S.O. Saliu, S.C. Sararu, JHEP 0310, 019 (2003) [20] G. Barnich, M. Henneaux, Phys. Lett. B 311, 123 (1993) [21] W. Pauli, M. Fierz, Helv. Phys. Acta 12, 297 (1939); M. Fierz, W. Pauli, Proc. Roy. Soc. Lond. A 173, 211 (1939) [22] G. Barnich, M. Henneaux, Mod. Phys. Lett. A 7, 2703 (1992) · Zbl 1021.81644 [23] M. Dubois-Violette, M. Henneaux, Lett. Math. Phys. 49, 245 (1999); Commun. Math. Phys. 226, 393 (2002) · Zbl 1096.18503 [24] G. Barnich, F. Brandt, M. Henneaux, Commun. Math. Phys. 174, 57 (1995); Phys. Rept. 338, 439 (2000) · Zbl 0844.53059 [25] N. Boulanger, T. Damour, L. Gualtieri, M. Henneaux, Nucl. Phys. B 597, 127 (2001) · Zbl 0972.83051 [26] G. Barnich, F. Brandt, M. Henneaux, Commun. Math. Phys. 174, 93 (1995); G. Barnich, M. Henneaux, Phys. Rev. Lett. 72, 1588 (1994) · Zbl 0844.53060 [27] C. Bizdadea, C.C. Ciobirca, E.M. Cioroianu, S.O. Saliu, S.C. Sararu, hep-th/0402099 [28] M. Henneaux, Commun. Math. Phys. 140, 1 (1991) · Zbl 0734.53067 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.