Unfolded form of conformal equations in M dimensions and o(M + 2)-modules

Reviews in Mathematical Physics

Volumn 18, Issue 8, 2006, Pages 823-886

  Shaynkman, O V ^a   Tipunin, I Yu ^a   Vasiliev, M A ^a  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

Author keywords

Conformal equations; Higher spin fields; Representation theory

Indexed keywords

EID: 33750735732     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0129055x06002814     Document Type: Review

References (52)

1. M. A. Vasiliev, Consistent equations for interacting massless fields of all spins in the first order in curvatures, Ann. Phys. (N. Y.) 190 (1989) 59-106.
2. M. A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 +1)dimensions, Phys. Lett. B 243 (1990) 378-382;
3. Properties of equations of motion of interacting gauge fields of all spins in (3 + 1)-dimensions, Class. Quant. Grav. 8 (1991) 1387-1417;
4. More on equations of motion for interacting massless fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 285 (1992) 225-234.
5. M. A. Vasiliev, Higher spin gauge theories: Star product AdS spacer, in The Many Faces of the Superworld; Golfand's Memorial Volume, ed. M. Shifman (World Scientific, 2000); arXiv: hep-th/9910096.
6. O. V. Shaynkman and M. A. Vasiliev, Scalar field in any dimension from the higher spin gauge theory perspective, Theor. Math. Phys. 123 (2000) 683-700; arXiv: hep-th/0003123.
7. M. A. Vasiliev, Conformal higher spin symmetries of 4-d massless supermultiplets and osp(L,2M) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006; arXiv: hep-th/0106149.
8. M. A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139-151; arXiv: hep-th/0304049.
9. E. S. Pradkin and V. Ya. Linetsky, BFV approach to geometric quantization, Nucl. Phys. B 431 (1994) 569-621.
10. B. V. Fedosov, Deformation Quantization and Index Theory, Berlin (Germany, Akademie-Verl, 1996).
11. M. A. Vasiliev, Higher-spin theories and Sp(2M) invariant space-time; arXiv: hep-th/0301235.
12. E. S. Fradkin and M. A. Vasiliev, Candidate to the role of higher spin symmetry, Ann. Phys. 177 (1987) 63-126.
13. S. E. Konstein and M. A. Vasiliev, Extended higher spin superalgebras and their massless representations, Nucl. Phys. B 331 (1990) 475-499.
14. E. S. Fradkin and V. Ya. Linetsky, A superconformal theory of massless higher spin fields in D = (2 + 1), Ann. Phys. 198 (1990) 293-320.
15. O. V. Shaynkman and M. A. Vasiliev, Higher spin conformal symmetry for matter fields in (2+ 1)-dimensions, Theor. Math. Phys. 128 (2001) 1155-1168; arXiv: hep-th/0103208.
16. E. Sezgin and P. Sundell, 7-D bosonic higher spin theory: Symmetry algebra and linearized constraints, Nucl. Phys. B 634 (2002) 120-140; arXiv: hep-th/0112100.
17. M. G. Eastwood, Higher symmetries of the Laplacian, Ann. of Math. 161(3) (2005) 1645-1665; arXiv: hep-th/0206233.
18. M. A. Vasiliev, Unfolded representation for relativistic equations in (2 + 1) anti-De Sitter space, Class. Quant. Grav. 11 (1994) 649-664.
19. D. A. Vogan, Representations of Real Reductive Lie Groups, Progress in Mathematics, Vol. 15 (Birkhauser, 1981).
20. A. Beilinson and J. Bernstein, A proof of the Jantzen conjectures, Advances in Soviet Mathematics, Vol. 16, Part 1 (AMS, 1993), pp. 1-50.
21. B. Kostant, Verma modules and the existence of quasi-invariant differential operators, Lect. Notes. Math. 466 (1975) 101-128.
22. M. G. Eastwood and J. W. Rice, Conformally invariant differential operators on Minkowski space and their curved analogues, Comm. Math. Phys. 109 (1987) 207-228; Erratum, Comm. Math. Phys. 144 (1992) 213.
23. T. Lada and J. Stasheff, Introduction to SH Lie algebras for physicists, Internat. J. Theoret. Phys. 32 (1993) 1087-1104; arXiv: hep-th/9209099.
24. H. Kajiura, Homotopy algebra morphism and geometry of classical string field theory, Nucl. Phys. B 630 (2002) 361-432; arXiv: hep-th/0112228.
25. M. A. Vasiliev, Triangle identity and free differential algebra of massless higher spins, Nucl. Phys. B 324 (1989) 503-522.
26. D. H. Mayer, Vector and tensor fields in conformal space, J. Math. Phys. 16(4) (1975) 884.
27. F. Bayen and M. Flato, Remarks on conformal space, J. Math. Phys. 17(7) (1976) 1112-1114.
28. V. B. Petkova, G. M. Sotkov and I. T. Todorov, Conformal gauges and renormalized equations of motion in massless quantum, Comm. Math. Phys. 97 (1985) 227-256.
29. E. S. Fradkin and M. Ya. Palchik, Conformal Quantum Field Theory in D-Dimensions (Kluwer Academic Publishers, 1996).
30. R. J. Baston and M. G. Eastwood, The Penrose Transform. Its Interaction with Representation Theory (Clarendon Press, Oxford, 1989).
31. M. A. Vasiliev, Extended higher spin superalgebras and their realizations in terms of quantum operators, Fortschr. Phys. 36 (1988) 33-62.
32. B. D. Boe and D. H. Collingwood, A comparison theory for the structure of induced representations, J. Algebra 54 (1985) 511-545.
33. B. D. Boe and D. H. Collingwood, A comparison theory for the structure of induced representations II, Math. Z. 190 (1985) 1-11.
34. T. P. Branson, An anomaly associated with 4-dimensional quantum gravity, Comm. Math. Phys. 178 (1996) 301-309.
35. T. Parker and S. Rosenberg, Invariants of conformal Laplacians, J. Diff. Geom. 25 (1987) 199-222.
36. R. J. Riegert, A nonlocal action for the trace anomaly, Phys. Lett. B 134 (1984) 56-60.
37. S. Paneitz, A quartic conformally covariant differential operators for arbitrary pseudo-Riemannian manifolds, MIT preprint (1983).
38. A. lorio, L. O'Raifeartaigh, I. Sachs and C. Wiesendanger, Weyl gauging and conformal invariance, Nucl. Phys. B 495 (1997) 433-450; arXiv: hep-th/9607110.
39. J. Erdmenger, Conformally covariant differential operators: Properties and applications, Class. Quant. Grav. 14 (1997) 2061-2084; arXiv: hep-th/9704108.
40. J. Erdmenger and H. Osborn, Conformally covariant differential operators: Symmetric tensor fields, Class. Quant. Grav. 15 (1998) 273-280; arXiv: gr-qc/9708040.
41. L. Dolan, C. R. Nappi and E. Witten, Conformal operators for partially massless states, JHEP 0110 (2001) 016; arXiv: hep-th/0109096.
42. W. Siegel, All free conformal representations in all dimensions, Int. J. Mod. Phys. A 4 (1989) 2015-2020.
43. R. R. Metsaev, All conformal invariant representations of d-dimensional anti-de Sitter group, Mod. Phys. Lett. A 10 (1995) 1719-1731.
44. S. Ferrara and C. Fronsdal, Conformal fields in higher dimensions, in Ninth Marcel Grossman Meeting, eds. V. G. Gurzadyan, R. T. Jantzen and R. Ruffini (World Scientific, 2002), pp. 508-527; arXiv: hep-th/0006009.
45. C. M. Hull, Symmetries and compactifications of (4,0) conformal gravity, JHEP (2000) 0012:007; arXiv: hep-th/0011215.
46. E. S. Fradkin and A. A. Tseytlin, Conformal supergravity, Phys. Rep. 119 (1985) 233-362.
47. A. Y. Segal, Conformai higher spin theory, Nucl. Phys. B 664 (2003) 59-130; arXiv: hep-th/0207212.
48. O. A. Gelfond and M. A. Vasiliev, Higher rank conformal fields in the sp(2m) symmetric generalized space-time, arXiv: hep-th/0304020.
49. G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in the antifield formalism. 1. General theorems, Commun. Math. Phys. 174 (1995) 57-92; arXiv: hep-th/9405109.
50. M. Dnbois-Violette and M. Henneaux, Tensor fields of mixed Young symmetry type and N complexes, Commun. Math. Phys. 226 (2002) 393-418; arXiv: math. QA/0110088.
51. V. G. Kac and D. A. Kazhdan, Structure of representations with highest weight of infinite-dimensional Lie algebras, Adv. Math. 34 (1984) 97-108.
52. D. P. Zhelobenko, Representations of Reductive Lie Algebras (Nauka, Fizmatlit Publishing Company, Moscow, 1993).