R4 counterterm and E7(7) symmetry in maximal supergravity

Journal of High Energy Physics

Volumn 2010, Issue 5, 2010, Pages

  Brödel, Johannes ^a,b   Dixon, Lance J ^c  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^c SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

Author keywords

Extended supersymmetry; Supergravity models

Indexed keywords

EID: 84856375984     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP05(2010)003     Document Type: Article

References (93)

1. G. 't Hooft and M. J. G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincare Phys. Theor. A 20 (1974) 69.
2. R. E. Kallosh, The renormalization in nonabelian gauge theories, Nucl. Phys. B 78 (1974) 293.
3. P. van Nieuwenhuizen and C. C. Wu, On integral relations for invariants constructed from three Riemann tensors and their applications in quantum gravity, J. Math. Phys. 18 (1977) 182.
4. M. H. Goroff and A. Sagnotti, The ultraviolet behavior of Einstein gravity, Nucl. Phys. B 266 (1986) 709.
5. A. E. M. van de Ven, Two loop quantum gravity, Nucl. Phys. B 378 (1992) 309.
6. M. T. Grisaru, Two loop renormalizability of supergravity, Phys. Lett. B 66 (1977) 75.
7. S. Deser, J. H. Kay and K. S. Stelle, Renormalizability properties of supergravity, Phys. Rev. Lett. 38 (1977) 527.
8. E. Tomboulis, On the two loop divergences of supersymmetric gravitation, Phys. Lett. B 67 (1977) 417.
9. M. T. Grisaru, H. N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S matrix, Phys. Rev. D 15 (1977) 996.
10. M. T. Grisaru and H. N. Pendleton, Some properties of scattering amplitudes in supersymmetric theories, Nucl. Phys. B 124 (1977) 81.
11. S. J. Parke and T. R. Taylor, Perturbative QCD utilizing extended supersymmetry, Phys. Lett. B 157 (1985) 81
12. [Erratum ibid. B 174 (1986) 465].
13. Z. Kunszt, Combined use of the Calkul method and N = 1 supersymmetry to calculate QCD six parton processes, Nucl. Phys. B 271 (1986) 333.
14. S. Ferrara and B. Zumino, Structure of conformal supergravity, Nucl. Phys. B 134 (1978) 301.
15. S. Deser and J. H. Kay, Three loop counterterms for extended supergravity, Phys. Lett. B 76 (1978) 400.
16. P. S. Howe and U. Lindström, Higher order invariants in extended supergravity, Nucl. Phys. B 181 (1981) 487.
17. R. E. Kallosh, Counterterms in extended supergravities, Phys. Lett. B 99 (1981) 122.
18. J. H. Schwarz, Superstring theory, Phys. Rept. 89 (1982) 223.
19. I. Robinson, unpublished.
20. L. Bel, Sur la radiation gravitationnelle (in French), Acad. Sci. Paris Comptes Rend. 247 (1958) 1094.
21. L. Bel, Introduction d'un tenseur du quatrieme order (in French), Acad. Sci. Paris Comptes Rend. 248 (1959) 1297.
22. D. J. Gross and E. Witten, Superstring modifications of Einstein's equations, Nucl. Phys. B 277 (1986) 1.
23. M. B. Green, J. H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 supergravity as limits of string theories, Nucl. Phys. B 198 (1982) 474.
24. K. Peeters, P. Vanhove and A. Westerberg, Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace, Class. Quant. Grav. 18 (2001) 843 [hep-th/0010167].
25. 4 terms in supergravity and M-theory, hep-th/0408177.
26. M. B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59 (1999) 046006 [hep-th/9808061].
27. E. Cremmer and B. Julia, The N = 8 supergravity theory. 1. The Lagrangian, Phys. Lett. B 80 (1978) 48.
28. E. Cremmer and B. Julia, The SO (8) supergravity, Nucl. Phys. B 159 (1979) 141.
29. P. S. Howe, K. S. Stelle and P. K. Townsend, Miraculous ultraviolet cancellations in supersymmetry made manifest, Nucl. Phys. B 236 (1984) 125.
30. P. S. Howe and K. S. Stelle, Supersymmetry counterterms revisited, Phys. Lett. B 554 (2003) 190 [hep-th/0211279].
31. A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained off-shell N = 3 supersymmetric Yang-Mills theory, Class. Quant. Grav. 2 (1985) 155.
32. Z. Bern, L. J. Dixon, D. C. Dunbar, M. Perelstein and J. S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [hep-th/9802162].
33. Z. Bern et al., Three-loop superfiniteness of N = 8 supergravity, Phys. Rev. Lett. 98 (2007) 161303 [hep-th/0702112].
34. Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson and R. Roiban, Manifest ultraviolet behavior for the three-loop four-point amplitude of N = 8 supergravity, Phys. Rev. D 78 (2008) 105019 [arXiv:0808.4112].
35. Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson and R. Roiban, The ultraviolet behavior of N = 8 supergravity at four loops, Phys. Rev. Lett. 103 (2009) 081301 [arXiv:0905.2326].
36. D. M. Richards, The one-loop five-graviton amplitude and the effective action, JHEP 10 (2008) 042 [arXiv:0807.2421].
37. R. Kallosh, On UV finiteness of the four loop N = 8 supergravity, JHEP 09 (2009) 116 [arXiv:0906.3495].
38. J. M. Drummond, P. J. Heslop, P. S. Howe and S. F. Kerstan, Integral invariants in N = 4 SYM and the effective action for coincident D-branes, JHEP 08 (2003) 016 [hep-th/0305202].
39. S. Stieberger, On tree-level higher order gravitational couplings in superstring theory, arXiv:0910.0180.
40. 4 theorems, Phys. Rev. Lett. 98 (2007) 211601 [hep-th/0609006].
41. M. B. Green, J. G. Russo and P. Vanhove, Ultraviolet properties of maximal supergravity, Phys. Rev. Lett. 98 (2007) 131602 [hep-th/0611273].
42. M. B. Green, J. G. Russo and P. Vanhove, String theory dualities and supergravity divergences, arXiv:1002.3805.
43. G. Chalmers, On the finiteness of N = 8 quantum supergravity, hep-th/0008162.
44. M. B. Green, J. G. Russo and P. Vanhove, Non-renormalisation conditions in type-II string theory and maximal supergravity, JHEP 02 (2007) 099 [hep-th/0610299].
45. M. B. Green, H. Ooguri and J. H. Schwarz, Decoupling supergravity from the superstring, Phys. Rev. Lett. 99 (2007) 041601 [arXiv:0704.0777].
46. Z. Bern, L. J. Dixon, M. Perelstein and J. S. Rozowsky, Multi-leg one-loop gravity amplitudes from gauge theory, Nucl. Phys. B 546 (1999) 423 [hep-th/9811140].
47. Z. Bern, N. E. J. Bjerrum-Bohr and D. C. Dunbar, Inherited twistor-space structure of gravity loop amplitudes, JHEP 05 (2005) 056 [hep-th/0501137].
48. N. E. J. Bjerrum-Bohr, D. C. Dunbar, H. Ita, W. B. Perkins and K. Risager, The no-triangle hypothesis for N = 8 supergravity, JHEP 12 (2006) 072 [hep-th/0610043].
49. N. E. J. Bjerrum-Bohr and P. Vanhove, Absence of triangles in maximal supergravity amplitudes, JHEP 10 (2008) 006 [arXiv:0805.3682].
50. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, arXiv:0808.1446.
51. Z. Bern, L. J. Dixon and R. Roiban, Is N = 8 supergravity ultraviolet finite?, Phys. Lett. B 644 (2007) 265 [hep-th/0611086].
52. Z. Bern, J. J. Carrasco, D. Forde, H. Ita and H. Johansson, Unexpected cancellations in gravity theories, Phys. Rev. D 77 (2008) 025010 [arXiv:0707.1035].
53. N. E. J. Bjerrum-Bohr and P. Vanhove, On cancellations of ultraviolet divergences in supergravity amplitudes, Fortsch. Phys. 56 (2008) 824 [arXiv:0806.1726].
54. S. Badger, N. E. J. Bjerrum-Bohr and P. Vanhove, Simplicity in the structure of QED and gravity amplitudes, JHEP 02 (2009) 038 [arXiv:0811.3405].
55. E. Cremmer, B. Julia and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B 76 (1978) 409.
56. 7 (7) on the light cone, JHEP 06 (2008) 034
57. [AIP Conf. Proc. 1078 (2009) 447] [arXiv:0801.2993].
58. 7 (7) on N = 8 supergravity fields, Nucl. Phys. B 801 (2008) 25 [arXiv:0802.4106].
59. 7 (7) invariant Lagrangian of d = 4 N = 8 supergravity, JHEP 04 (2010) 010 [arXiv:0911.5225].
60. G. Bossard, P. S. Howe and K. S. Stelle, A note on the UV behaviour of maximally supersymmetric Yang-Mills theories, Phys. Lett. B 682 (2009) 137 [arXiv:0908.3883].
61. R. E. Kallosh, Counterterms in extended supergravities, in Proceedings of Quantum Gravity, Moscow Russia (1981), pg. 415.
62. R. Kallosh, N = 8 supergravity on the light cone, Phys. Rev. D 80 (2009) 105022 [arXiv:0903.4630].
63. M. Bianchi, H. Elvang and D. Z. Freedman, Generating tree amplitudes in N = 4 SYM and N = 8 SG, JHEP 09 (2008) 063 [arXiv:0805.0757].
64. S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current, Phys. Rev. 137 (1965) B1022.
65. S. Coleman, Secret symmetry: an introduction to spontaneous symmetry breakdown and gauge fields, in Aspects of symmetry: selected Erice lectures of Sidney Coleman, Cambridge University Press, Cambridge U. K. (1985)
66. [Subnucl. Ser. 11 (1975) 139].
67. N. Marcus, Composite anomalies in supergravity, Phys. Lett. B 157 (1985) 383.
68. 7 (7) symmetry, arXiv:0812.4533.
69. R. Kallosh, C. H. Lee and T. Rube, N = 8 supergravity 4-point amplitudes, JHEP 02 (2009) 050 [arXiv:0811.3417].
70. J. Kaplan, private communication.
71. S. Stieberger and T. R. Taylor, Complete six-gluon disk amplitude in superstring theory, Nucl. Phys. B 801 (2008) 128 [arXiv:0711.4354].
72. H. Kawai, D. C. Lewellen and S. H. Henry Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1.
73. B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323.
74. R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308].
75. R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052].
76. 7 in amplitudes of N = 8 supergravity, JHEP 01 (2009) 072 [arXiv:0811.3414].
77. V. P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B 214 (1988) 215.
78. M. L. Mangano and S. J. Parke, Multi-parton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223].
79. S. J. Parke and T. R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56 (1986) 2459.
80. J. M. Drummond and J. M. Henn, All tree-level amplitudes in N = 4 SYM, JHEP 04 (2009) 018 [arXiv:0808.2475].
81. F. A. Berends, W. T. Giele and H. Kuijf, On relations between multi-gluon and multigraviton scattering, Phys. Lett. B 211 (1988) 91.
82. J. M. Drummond, M. Spradlin, A. Volovich and C. Wen, Tree-level amplitudes in N = 8 supergravity, Phys. Rev. D 79 (2009) 105018 [arXiv:0901.2363].
83. J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [arXiv:0807.1095].
84. M. B. Green and J. H. Schwarz, Supersymmetrical dual string theory. 2. Vertices and trees, Nucl. Phys. B 198 (1982) 252.
85. A. A. Tseytlin, Vector field effective action in the open superstring theory, Nucl. Phys. B 276 (1986) 391
86. [Erratum ibid. B 291 (1987) 876].
87. D. Oprisa and S. Stieberger, Six gluon open superstring disk amplitude, multiple hypergeometric series and Euler-Zagier sums, hep-th/0509042.
88. S. Stieberger and T. R. Taylor, Amplitude for N-gluon superstring scattering, Phys. Rev. Lett. 97 (2006) 211601 [hep-th/0607184].
89. S. Stieberger and T. R. Taylor, Multi-gluon scattering in open superstring theory, Phys. Rev. D 74 (2006) 126007 [hep-th/0609175].
90. H. Elvang, D. Z. Freedman and M. Kiermaier, Solution to the Ward identities for superamplitudes, arXiv:0911.3169.
91. L. J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359.
92. S. Stieberger and T. R. Taylor, Supersymmetry relations and MHV amplitudes in superstring theory, Nucl. Phys. B 793 (2008) 83 [arXiv:0708.0574].
93. M. F. Sohnius, Introducing supersymmetry, Phys. Rept. 128 (1985) 39.