Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence

Journal of High Energy Physics

Volumn 4, Issue 2, 2000, Pages 1-20

  Bastianelli, Fiorenzo ^a   Frolov, Sergei ^b,d   Tseytlin, Arkady A ^c,e,f  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF ALABAMA   (United States)

^c OHIO STATE UNIVERSITY   (United States)

^d STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^e LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

^f IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

1 N Expansion; Field Theories in Higher Dimensions; M Theory

Indexed keywords

EID: 7044233648     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/02/013     Document Type: Article

References (75)

1. I.R. Klebanov and A.A. Tseytlin, Entropy of near-extremal black p-branes, Nucl. Phys. B 475 (1996) 164 [hep-th/9604089].
2. S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, String theory and classical absorption by three-branes, Nucl. Phys. B 499 (1997) 217 [hep-th/9703040].
3. S.S. Gubser and I.R. Klebanov, Absorption by branes and Schwinger terms in the world volume theory, Phys. Lett. B 413 (1997) 41 [hep-th/9708005].
4. J. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200].
5. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109].
6. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150].
7. 11-p and superconformal field theories, Phys. Lett. B 430 (1998) 87 [hep-th/9803051].
8. 2/5 brane worldvolumes, J. High Energy Phys. 10 (1998) 002 [hep-th/9803063].
9. R.G. Leigh and M. Rozali, The large-N limit of the (2,0) superconformal field theory, Phys. Lett. B 431 (1998) 311 [hep-th/9803068].
10. 7/4 and M-branes, J. High Energy Phys. 04 (1998) 011 [hep-th/9803077].
11. M. Henningson and K. Skenderis, The holographic Weyl anomaly, J. High Energy Phys. 07 (1998) 023 [hep-th/9806087].
12. J.A. Harvey, R. Minasian and G. Moore, Non-abelian tensor-multiplet anomalies, J. High Energy Phys. 09 (1998) 004 [hep-th/9808060].
13. 6 correspondence and matrix models of M5-branes, Adv. Theor. Math. Phys. 3 (1999) 147 [hep-th/9812218].
14. C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [hep-th/9901021]; M. Henningson and K. Skenderis, Weyl anomaly for Wilson surfaces, J. High Energy Phys. 06 (1999) 012 [hep-th/9905163].
15. C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [hep-th/9901021]; M. Henningson and K. Skenderis, Weyl anomaly for Wilson surfaces, J. High Energy Phys. 06 (1999) 012 [hep-th/9905163].
16. G. Arutyunov and S. Frolov, Three-point Green function of the stress-energy tensor in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 026004 [hep-th/9901121].
17. R. Corrado, B. Florea and R. McNees, Correlation functions of operators and Wilson surfaces in the D = 6, (0,2) theory in the large-N limit, Phys. Rev. D 60 (1999) 085011 [hep-th/9902153].
18. 4/7, Class. and Quant. Grav. 16 (1999) 3673 [hep-th/9903161]; Three point functions of chiral primary operators in D = 3, N = 8 and D = 6, N = (2,0) SCFT at large-N, Phys. Lett. B 467 (1999) 61 [hep-th/9907047]; Three point functions for a class of chiral operators in maximally supersymmetric CFT at large-N, hep-th/9909179.
19. 4/7, Class. and Quant. Grav. 16 (1999) 3673 [hep-th/9903161]; Three point functions of chiral primary operators in D = 3, N = 8 and D = 6, N = (2,0) SCFT at large-N, Phys. Lett. B 467 (1999) 61 [hep-th/9907047]; Three point functions for a class of chiral operators in maximally supersymmetric CFT at large-N, hep-th/9909179.
20. 4/7, Class. and Quant. Grav. 16 (1999) 3673 [hep-th/9903161]; Three point functions of chiral primary operators in D = 3, N = 8 and D = 6, N = (2,0) SCFT at large-N, Phys. Lett. B 467 (1999) 61 [hep-th/9907047]; Three point functions for a class of chiral operators in maximally supersymmetric CFT at large-N, hep-th/9909179.
21. 4 reduction and the origin of self-duality in odd dimensions, hep-th/9911238.
22. 4 reduction and the origin of self-duality in odd dimensions, hep-th/9911238.
23. 6 correspondence, hep-th/9910192.
24. C. Imbimbo, A. Schwimmer, S. Theisen and S. Yankielowicz, Diffeomorphisms and holographic anomalies, hep-th/9910267.
25. F. Bastianelli, S. Frolov and A.A. Tseytlin, Three-point correlators of stress tensors in maximally- supersymmetric conformal theories in D = 3 and D = 6, hep-th/9911135.
26. H. Liu and A.A. Tseytlin, D = 4 super Yang-Mills, d = 5 gauged supergravity and d = 4 conformal supergravity, Nucl. Phys. B 533 (1998) 88 [hep-th/9804083].
27. H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Ann. Phys. (NY) 231 (1994) 311 [hep-th/9307010]; J. Erdmenger and H. Osborn, Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009].
28. H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Ann. Phys. (NY) 231 (1994) 311 [hep-th/9307010]; J. Erdmenger and H. Osborn, Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009].
29. R. Graham, "Volume and area renormalizations for conformally compact Einstein metrics", math.DG/9909042.
30. M.J. Duff, Observations on conformal anomalies, Nucl. Phys. B 125 (1977) 334; Twenty years of the Weyl anomaly, Class. and Quant. Grav. 11 (1994) 1387 [hep-th/9308075].
31. M.J. Duff, Observations on conformal anomalies, Nucl. Phys. B 125 (1977) 334; Twenty years of the Weyl anomaly, Class. and Quant. Grav. 11 (1994) 1387 [hep-th/9308075].
32. S. Deser, M.J. Duff and C.J. Isham, Nonlocal conformal anomalies, Nucl. Phys. B 111 (1976) 45.
33. L. Bonora, P. Pasti and M. Bregola, Weyl cocycles, Class. and Quant. Grav. 3 (1986) 635.
34. S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047].
35. D.R. Karakhanian, R.P. Manvelian and R.L. Mkrtchian, Trace anomalies and cocycles of Weyl and diffeomorphism groups, Mod. Phys. Lett. A 11 (1996) 409 [hep-th/9411068]; T. Arakelian, D.R. Karakhanian, R.P. Manvelian and R.L. Mkrtchian, Trace anomalies and cocycles of the Weyl group, Phys. Lett. B 353 (1995) 52; S.D. Odintsov and A. Romeo, Conformal sector in D = 6 quantum gravity, Mod. Phys. Lett. A 9 (1994) 3373 [hep-th/9410191].
36. D.R. Karakhanian, R.P. Manvelian and R.L. Mkrtchian, Trace anomalies and cocycles of Weyl and diffeomorphism groups, Mod. Phys. Lett. A 11 (1996) 409 [hep-th/9411068]; T. Arakelian, D.R. Karakhanian, R.P. Manvelian and R.L. Mkrtchian, Trace anomalies and cocycles of the Weyl group, Phys. Lett. B 353 (1995) 52; S.D. Odintsov and A. Romeo, Conformal sector in D = 6 quantum gravity, Mod. Phys. Lett. A 9 (1994) 3373 [hep-th/9410191].
37. D.R. Karakhanian, R.P. Manvelian and R.L. Mkrtchian, Trace anomalies and cocycles of Weyl and diffeomorphism groups, Mod. Phys. Lett. A 11 (1996) 409 [hep-th/9411068]; T. Arakelian, D.R. Karakhanian, R.P. Manvelian and R.L. Mkrtchian, Trace anomalies and cocycles of the Weyl group, Phys. Lett. B 353 (1995) 52; S.D. Odintsov and A. Romeo, Conformal sector in D = 6 quantum gravity, Mod. Phys. Lett. A 9 (1994) 3373 [hep-th/9410191].
38. 4, Phys. Lett. B 394 (1997) 329 [hep-th/9608125]; P.S. Howe, E. Sokatchev and P.C. West, 3-point functions in N = 4 Yang-Mills, Phys. Lett. B 444 (1998) 341 [hep-th/9808162].
39. 4, Phys. Lett. B 394 (1997) 329 [hep-th/9608125]; P.S. Howe, E. Sokatchev and P.C. West, 3-point functions in N = 4 Yang-Mills, Phys. Lett. B 444 (1998) 341 [hep-th/9808162].
40. 4, Phys. Lett. B 394 (1997) 329 [hep-th/9608125]; P.S. Howe, E. Sokatchev and P.C. West, 3-point functions in N = 4 Yang-Mills, Phys. Lett. B 444 (1998) 341 [hep-th/9808162].
41. X. Bekaert, M. Henneaux and A. Sevrin, Deformations of chiral two-forms in six dimensions, Phys. Lett. B 468 (1999) 228 [hep-th/9909094]; X. Bekaert, Interactions of chiral two-forms, hep-th/9911109.
42. X. Bekaert, M. Henneaux and A. Sevrin, Deformations of chiral two-forms in six dimensions, Phys. Lett. B 468 (1999) 228 [hep-th/9909094]; X. Bekaert, Interactions of chiral two-forms, hep-th/9911109.
43. S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [hep-th/9805156].
44. S. Deser, Closed form effective conformal anomaly actions in D ≥ 4, hep-th/9911129.
45. D. Anselmi, Towards the classification of conformal field theories in arbitrary dimension, hep-th/9908014.
46. A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207; Quantum gravity in two-dimensions, Mod. Phys. Lett. A 2 (1987) 893.
47. A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207; Quantum gravity in two-dimensions, Mod. Phys. Lett. A 2 (1987) 893.
48. R.J. Riegert, A nonlocal action for the trace anomaly, Phys. Lett. B 134 (1984) 56.
49. E.S. Fradkin and A.A. Tseytlin, Conformal anomaly in Weyl theory and anomaly free superconformal theories, Phys. Lett. B 134 (1984) 187.
50. J. Erdmenger, Conformally covariant differential operators: properties and applications, Class. and Quant. Grav. 14 (1997) 2061 [hep-th/9704108]; J. Erdmenger and H. Osborn, Conformally covariant differential operators: symmetric tensor fields, Class. and Quant. Grav. 15 (1998) 273 [gr-qc/9708040].
51. J. Erdmenger, Conformally covariant differential operators: properties and applications, Class. and Quant. Grav. 14 (1997) 2061 [hep-th/9704108]; J. Erdmenger and H. Osborn, Conformally covariant differential operators: symmetric tensor fields, Class. and Quant. Grav. 15 (1998) 273 [gr-qc/9708040].
52. E.S. Fradkin and A.A. Tseytlin, Quantum properties of higher dimensional and dimensionally reduced supersymmetric theories, Nucl. Phys. B 227 (1983) 252.
53. T. Sakai, On eigenvalues of laplacean and curvature of riemannian manifold, Tohoku Math. J. 23 (1971) 589.
54. P.B. Gilkey, Spectral geometry of a Riemann manifold, J. Diff. Geom. 10 (1975) 601.
55. J.S. Dowker, Single-loop divergences in six dimensions, J. Phys. A10 (1977) L63.
56. R. Critchley, The trace anomaly: results for spinor fields in six-dimensions, J. Phys. A11 (1978) 1113.
57. M.J. Duff and P. van Nieuwenhuizen, Quantum inequivalence of different field representations, Phys. Lett. B 94 (1980) 179.
58. D.J. Toms, Renormalization of interacting scalar field theories in curved space-time, Phys. Rev. D 26 (1982) 2713.
59. D. Anselmi, Quantum irreversibility in arbitrary dimension, hep-th/9905005.
60. T. Parker and S. Rosenberg, Invariants of conformal laplaceans, J. Diff. Geom. 25 (1987) 199.
61. S. Ichinose and N. Ikeda, Weyl anomaly in higher dimensions and Feynman rules in coordinate space, J. Math. Phys. 40 (1999) 2259 [hep-th/9810256].
62. L. Alvarez-Gaume and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269.
63. E. Witten, Five-brane effective action in M-theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234]; L. Dolan and C.R. Nappi, A modular invariant partition function for the fivebrane, Nucl. Phys. B 530 (1998) 683 [hep-th/9806016].
64. E. Witten, Five-brane effective action in M-theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234]; L. Dolan and C.R. Nappi, A modular invariant partition function for the fivebrane, Nucl. Phys. B 530 (1998) 683 [hep-th/9806016].
65. M. Henningson, B.E. W. Nilsson and P. Salomonson, Holomorphic factorization of correlation functions in (4k + 2)-dimensional (2k)-form gauge theory, J. High Energy Phys. 09 (1999) 008 [hep-th/9908107].
66. B.S. De Witt, Dynamical theory of groups and fields, Gordon and Breach, New York 1965.
67. R.T. Seeley, Complex powers of an elliptic operator, Proc. Symp. Pure. Appl. Math. 10 (1967) 288.
68. A.S. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247; W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170; J. Thierry-Mieg, BRS structure of the antisymmetric tensor gauge theories, Nucl. Phys. B 335 (1990) 334; E. Sezgin and P. van Nieuwenhuizen, Renormalizability properties of antisymmetric tensor fields coupled to gravity, Phys. Rev. D 22 (1980) 301; Y.N. Obukhov, The geometrical approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195; A.S. Schwarz and Y.S. Tyupkin, Quantization of antisymmetric tensors and ray-singer torsion, Nucl. Phys. B 242 (1984) 436.
69. A.S. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247; W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170; J. Thierry-Mieg, BRS structure of the antisymmetric tensor gauge theories, Nucl. Phys. B 335 (1990) 334; E. Sezgin and P. van Nieuwenhuizen, Renormalizability properties of antisymmetric tensor fields coupled to gravity, Phys. Rev. D 22 (1980) 301; Y.N. Obukhov, The geometrical approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195; A.S. Schwarz and Y.S. Tyupkin, Quantization of antisymmetric tensors and ray-singer torsion, Nucl. Phys. B 242 (1984) 436.
70. A.S. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247; W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170; J. Thierry-Mieg, BRS structure of the antisymmetric tensor gauge theories, Nucl. Phys. B 335 (1990) 334; E. Sezgin and P. van Nieuwenhuizen, Renormalizability properties of antisymmetric tensor fields coupled to gravity, Phys. Rev. D 22 (1980) 301; Y.N. Obukhov, The geometrical approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195; A.S. Schwarz and Y.S. Tyupkin, Quantization of antisymmetric tensors and ray-singer torsion, Nucl. Phys. B 242 (1984) 436.
71. A.S. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247; W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170; J. Thierry-Mieg, BRS structure of the antisymmetric tensor gauge theories, Nucl. Phys. B 335 (1990) 334; E. Sezgin and P. van Nieuwenhuizen, Renormalizability properties of antisymmetric tensor fields coupled to gravity, Phys. Rev. D 22 (1980) 301; Y.N. Obukhov, The geometrical approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195; A.S. Schwarz and Y.S. Tyupkin, Quantization of antisymmetric tensors and ray-singer torsion, Nucl. Phys. B 242 (1984) 436.
72. A.S. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247; W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170; J. Thierry-Mieg, BRS structure of the antisymmetric tensor gauge theories, Nucl. Phys. B 335 (1990) 334; E. Sezgin and P. van Nieuwenhuizen, Renormalizability properties of antisymmetric tensor fields coupled to gravity, Phys. Rev. D 22 (1980) 301; Y.N. Obukhov, The geometrical approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195; A.S. Schwarz and Y.S. Tyupkin, Quantization of antisymmetric tensors and ray-singer torsion, Nucl. Phys. B 242 (1984) 436.
73. A.S. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247; W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170; J. Thierry-Mieg, BRS structure of the antisymmetric tensor gauge theories, Nucl. Phys. B 335 (1990) 334; E. Sezgin and P. van Nieuwenhuizen, Renormalizability properties of antisymmetric tensor fields coupled to gravity, Phys. Rev. D 22 (1980) 301; Y.N. Obukhov, The geometrical approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195; A.S. Schwarz and Y.S. Tyupkin, Quantization of antisymmetric tensors and ray-singer torsion, Nucl. Phys. B 242 (1984) 436.
74. F. Bastianelli, The path integral for a particle in curved spaces and Weyl anomalies, Nucl. Phys. B 376 (1992) 113 [hep-th/9112035].
75. F. Bastianelli and P. van Nieuwenhuizen, Trace anomalies from quantum mechanics, Nucl. Phys. B 389 (1993) 53 [hep-th/9208059].