Theory of higher spin tensor currents and central charges

Nuclear Physics B

Volumn 541, Issue 1-2, 1999, Pages 323-368

  Anselmi, Damiano ^a,b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b CERN   (Switzerland)

Author keywords

Anomalies; Composite operators; Conformal field theory; Current algebra; Higher spin fields; Higher spin symmetries; Operator product expansion; Quantum field theory; Renormalization; Renormalization group

Indexed keywords

EID: 0033593775     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00783-4     Document Type: Article

References (38)

1. N. Seiberg, Electric-magnetic duality in supersymmetric non-abelian gauge theories, Nucl. Phys. B 435 (1995) 129.
2. D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Non-perturbative formulas for central functions in supersymmetric theories, Nucl. Phys. B and hepth/9708042.
3. D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 7570 and hepth/9711035.
4. D. Anselmi, Central functions and their physical implications, JHEP 05 (1998) 005 and hep-th/9702056.
5. 4, Nucl. Phys. B 491 (1997) 221 and hepth/9601023.
6. 4, Phys. Lett. B 324 (1997) 329.
7. See, for example, T. Muta, Foundations of Quantum Chromodynamics: An Introduction to Perturbative Methods in Gauge Theories (World Scientific, Singapore, 1987).
8. J.M. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity, hepth/9705104.
9. R. Jackiw, in Current Algebra and Anomalies, ed. S.B. Treiman et al. (World Scientific, Singapore, 1985).
10. F.A. Berends, G.J.H. Burgers and H. Van Dam, Explicit construction of conserved currents for massless fields of arbitrary spin, Nucl. Phys. B 271 (1986) 429; On the theoretical problem in constructing interactions involving higher-spin massless particles, Nucl. Phys. B 260 (1985) 295.
11. F.A. Berends, G.J.H. Burgers and H. Van Dam, Explicit construction of conserved currents for massless fields of arbitrary spin, Nucl. Phys. B 271 (1986) 429; On the theoretical problem in constructing interactions involving higher-spin massless particles, Nucl. Phys. B 260 (1985) 295.
12. M.A. Vasiliev, Higher spin gauge theories in four, three and two dimensions, Int. J. Mod. Phys. D 5 (1996) 763 and hep-th/9611024.
13. L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. I. The boson case, Phys. Rev. D 9 (1974) 898; C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624; Singleton and massless,integral spin fields on de sitter space (elementary particles in a curved space VII), Phys. Rev. D 20 (1979) 848; T. Curtright, Massless spin supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979) 219; M.A. Vasiliev, Sov. J. Nucl. Phys. 32 (1980) 855 (p. 439 in English transl.); C. Aragone and S. Deser, Higher spin vierbein gauge fermions and hypergravities, Nucl. Phys. B 170 [FSI] (1980) 329.
14. L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. I. The boson case, Phys. Rev. D 9 (1974) 898; C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624; Singleton and massless,integral spin fields on de sitter space (elementary particles in a curved space VII), Phys. Rev. D 20 (1979) 848; T. Curtright, Massless spin supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979) 219; M.A. Vasiliev, Sov. J. Nucl. Phys. 32 (1980) 855 (p. 439 in English transl.); C. Aragone and S. Deser, Higher spin vierbein gauge fermions and hypergravities, Nucl. Phys. B 170 [FSI] (1980) 329.
15. L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. I. The boson case, Phys. Rev. D 9 (1974) 898; C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624; Singleton and massless, integral spin fields on de sitter space (elementary particles in a curved space VII), Phys. Rev. D 20 (1979) 848; T. Curtright, Massless spin supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979) 219; M.A. Vasiliev, Sov. J. Nucl. Phys. 32 (1980) 855 (p. 439 in English transl.); C. Aragone and S. Deser, Higher spin vierbein gauge fermions and hypergravities, Nucl. Phys. B 170 [FSI] (1980) 329.
16. L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. I. The boson case, Phys. Rev. D 9 (1974) 898; C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624; Singleton and massless,integral spin fields on de sitter space (elementary particles in a curved space VII), Phys. Rev. D 20 (1979) 848; T. Curtright, Massless spin supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979) 219; M.A. Vasiliev, Sov. J. Nucl. Phys. 32 (1980) 855 (p. 439 in English transl.); C. Aragone and S. Deser, Higher spin vierbein gauge fermions and hypergravities, Nucl. Phys. B 170 [FSI] (1980) 329.
17. L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. I. The boson case, Phys. Rev. D 9 (1974) 898; C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624; Singleton and massless,integral spin fields on de sitter space (elementary particles in a curved space VII), Phys. Rev. D 20 (1979) 848; T. Curtright, Massless spin supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979) 219; M.A. Vasiliev, Sov. J. Nucl. Phys. 32 (1980) 855 (p. 439 in English transi.); C. Aragone and S. Deser, Higher spin vierbein gauge fermions and hypergravities, Nucl. Phys. B 170 [FSI] (1980) 329.
18. L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. I. The boson case, Phys. Rev. D 9 (1974) 898; C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624; Singleton and massless,integral spin fields on de sitter space (elementary particles in a curved space VII), Phys. Rev. D 20 (1979) 848; T. Curtright, Massless spin supermultiplets with arbitrary spin, Phys. Lett. B 85 (1979) 219; M.A. Vasiliev, Sov. J. Nucl. Phys. 32 (1980) 855 (p. 439 in English transi.); C. Aragone and S. Deser, Higher spin vierbein gauge fermions and hypergravities, Nucl. Phys. B 170 [FSI] (1980) 329.
19. B. de Wit and D.Z. Freedman, Systematics of higher spin gauge fields, Phys. Rev. D 21 (1980) 358.
20. S. Ferrara, R. Gatto and A.F. Grillo, Conformal Algebra in Space-time (Springer, Berlin, 1967); S. Ferrara, A.F. Grillo and G. Parisi, The shadow operator formalism for conformal algebra. Vacuum expectation values of operator products, Lett. Nuovo Cimento 4 (1972) 115; S. Ferrara, R. Gatto, A.F. Grillo and G. Parisi, Canonical scaling and conformal invariance, Phys. Lett. B 38 (1972) 333.
21. S. Ferrara, R. Gatto and A.F. Grillo, Conformal Algebra in Space-time (Springer, Berlin, 1967); S. Ferrara, A.F. Grillo and G. Parisi, The shadow operator formalism for conformal algebra. Vacuum expectation values of operator products, Lett. Nuovo Cimento 4 (1972) 115; S. Ferrara, R. Gatto, A.F. Grillo and G. Parisi, Canonical scaling and conformal invariance, Phys. Lett. B 38 (1972) 333.
22. S. Ferrara, R. Gatto and A.F. Grillo, Conformal Algebra in Space-time (Springer, Berlin, 1967); S. Ferrara, A.F. Grillo and G. Parisi, The shadow operator formalism for conformal algebra. Vacuum expectation values of operator products, Lett. Nuovo Cimento 4 (1972) 115; S. Ferrara, R. Gatto, A.F. Grillo and G. Parisi, Canonical scaling and conformal invariance, Phys. Lett. B 38 (1972) 333.
23. See, for example, E.J. Schreier, Conformal symmetry and three-point functions, Phys. Rev. D 3 (1971) 980; M. Baker and K. Johnson, Applications of conformal symmetry in quantum electrodynamics, Physica A 96 (1979) 120.
24. See, for example, E.J. Schreier, Conformal symmetry and three-point functions, Phys. Rev. D 3 (1971)980; M. Baker and K. Johnson, Applications of conformal symmetry in quantum electrodynamics, Physica A 96 (1979) 120.
25. D. Anselmi, Higher Spin Anomalies, to appear.
26. J.C. Collins, Renormalization (Cambridge Univ. Press, Cambridge, 1985).
27. See Refs. [20,5] and A.C. Petkou, Conserved currents, consistency relations and operator product expansions in the conformally invariant O(N) vector model, Ann. Phys. 249 (1996) 180.
28. S. Ferrara, R. Gatto and A.F. Grillo, Conformal invariance on the light cone and canonical dimensions, Nucl. Phys. B 34 (1971) 349.
29. Y. Stanev, Stress energy tensor and U(1) current operator product expansions in conformal QFT, Bulg. J. Phys. 15 (1988) 93; H. Osborn and A. Petkov, Implications of conformal invariance in field theories for general dimensions. Ann. Phys. (NY) 231 (1994) 311.
30. Y. Stanev, Stress energy tensor and U(1) current operator product expansions in conformal QFT, Bulg. J. Phys. 15 (1988) 93; H. Osborn and A. Petkov, Implications of conformal invariance in field theories for general dimensions. Ann. Phys. (NY) 231 (1994) 311.
31. I. Antoniadis, P.O. Mazur and E. Mottola, Physical states of the quantum conformal factor, Phys. Rev. D 55 (1997) 4770.
32. K. Konishi, Anomalous supersymmetry transformations of some composite operators in SQCD, Phys. Lett. B 135 (1984) 439.
33. S. Ferrara and A. Zaffaroni, Bulk Gauge Fields in AdS Supergravity and Supersingletons, hepth/9807090.
34. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge Theory Correlators from Non-critical String Theory, hepth/9802109.
35. A.B. Zamolodchikov, "Irreversibility" of the flux of the renormalization group in a 2D field theory, JETP Lett. 43 (1986) 730.
36. S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace (Addison Wesley, Reading, MA, 1983).
37. D. Anselmi, The N = 4 quantum conformal algebra, Nucl. Phys. B 541 (1999) 369, next article in this issue, hep-th/9809192; D. Anselmi, Quantum Conformal Algebras and Closed Conformal Field Theory, CERN-TH/98-36, hep-th/9811149.
38. D. Anselmi, The N = 4 quantum conformal algebra, Nucl. Phys. B 541 (1999) 369, next article in this issue, hep-th/9809192; D. Anselmi, Quantum Conformal Algebras and Closed Conformal Field Theory, CERN-TH/98-36, hep-th/9811149.