All consistent interactions for exterior form gauge fields

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 56, Issue 10, 1997, Pages R6076-R6080

  Henneaux, Marc ^a   Knaepen, Bernard ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

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EID: 0001670833     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.56.R6076     Document Type: Article

References (27)

1. We include in the first category the interaction vertices that do not satisfy (Formula presented) off-shell, but can be made to do so by a field redefinition. Similarly, we include in the second category the interaction vertices that deform nontrivially the gauge transformations, but deform trivially their algebra, in the sense that the gauge algebra can be made Abelian by appropriate redefinition. This will always be understood in the sequel.
2. S. Deser, R. Jackiw, and S. Templeton, Phys. Rev. Lett. 48, 975 (1982).
3. D. Freedman and P. K. Townsend, Nucl. Phys. B177, 282 (1981).
4. S. Anco, J. Math. Phys. 36, 6553 (1995).
5. M. Henneaux, Phys. Lett. B 368, 83 (1996).
6. C. Teitelboim, Phys. Lett. 167B, 63 (1986).
7. See M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992).
8. M. Henneaux, Commun. Math. Phys. 140, 1 (1991).
9. G. Barnich, F. Brandt, and M. Henneaux, Commun. Math. Phys. 174, 57 (1995).
10. G. Barnich and M. Henneaux, Phys. Rev. Lett. 72, 1588 (1994);
11. G. Barnich, F. Brandt, and M. Henneaux, Commun. Math. Phys. 174, 93 (1995).
12. G. Barnich and M. Henneaux, Phys. Lett. B 311, 123 (1993).
13. J. Gomis and S. Weinberg, Nucl. Phys. B469, 473 (1996).
14. M. Henneaux, B. Knaepen, and C. Schomblond, Commun. Math. Phys. 186, 137 (1997).
15. M. Henneaux and B. Knaepen (in preparation).
16. J. D. Stasheff, q-alg/9702012.
17. G. F. Chapline and N. S. Manton, Phys. Lett. 120B, 105 (1983);
18. H. Nicolai and P. K. Townsend, 98B, 257 (1981);
19. A. H. Chamseddine, Nucl. Phys. B185, 403 (1981);
20. A. H. Chamseddine, Phys. Rev. D 24, 3065 (1981);
21. E. Bergshoeff, M. de Roo, B. de Witt, and P. van Nieuwenhuizen, Nucl. Phys. B195, 97 (1982).
22. With three (or more) different degrees, however, one may modify the algebra at order (Formula presented). For instance, if (Formula presented), (Formula presented), and (Formula presented) are, respectively, 3-, 4-, and 7-forms, the Lagrangian (Formula presented) is invariant under the gauge transformations (Formula presented), (Formula presented), and (Formula presented), where (Formula presented), (Formula presented), and (Formula presented) are, respectively, 2-, 3-, and 6-forms. Here, (Formula presented), (Formula presented) and (Formula presented). The commutator of two (Formula presented)-transformations is a (Formula presented)-transformation with (Formula presented). The fact that the gauge algebra may become non-Abelian at order (Formula presented) shows that the connection interpretation, which excludes this possibility, is not always appropriate.
23. F. Brandt and N. Dragon, “New Gauge Invariant Interactions of (Formula presented)-Form and (Formula presented)-Form Gauge Potentials,” hep-th/9709021.
24. F. Brandt, hep-th/9609192.
25. J. Thierry-Mieg, Nucl. Phys. B335, 334 (1990).
26. M. Henneaux, V. E. R. Lemes, C. A. G. Sasaki, S. P. Sorella, O. S. Ventura, and L. C. Q. Vilar, “A No-Go Theorem for the Nonabelian Topological Mass Mechanism in Four Dimensions,” hep-th/9707129.
27. S. Anco, J. Math. Phys. 38, 3393 (1997).