A simple approach to counterterms in N=8 supergravity

Journal of High Energy Physics

Volumn 2010, Issue 11, 2010, Pages

  Elvang, Henriette ^a,b   Freedman, Daniel Z ^c,d   Kiermaier, Michael ^e  

^a UNIVERSITY OF MICHIGAN   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^e PRINCETON UNIVERSITY   (United States)

Author keywords

Extended supersymmetry; Models of quantum gravity; Supergravity models; Supersymmetric gauge theory

Indexed keywords

EID: 78649728198     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP11(2010)016     Document Type: Article

References (58)

1. Z. Bern et al., Three-Loop Superfiniteness of N = 8 Supergravity, Phys. Rev. Lett. 98 (2007) 161303 [hep-th/0702112] [SPIRES].
2. 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] [SPIRES].
3. Z. Bern, J.J.M. Carrasco and H. Johansson, Progress on Ultraviolet Finiteness of Supergravity, arXiv:0902.3765 [SPIRES].
4. 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] [SPIRES].
5. 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] [SPIRES].
6. 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] [SPIRES].
7. N.E.J. Bjerrum-Bohr and P. Vanhove, Explicit Cancellation of Triangles in One-loop Gravity Amplitudes, JHEP 04 (2008) 065 [arXiv:0802.0868] [SPIRES].
8. N.E.J. Bjerrum-Bohr and P. Vanhove, Absence of Triangles in Maximal Supergravity Amplitudes, JHEP 10 (2008) 006 [arXiv:0805.3682] [SPIRES].
9. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].
10. P.S. Howe and U. Lindström, Higher Order Invariants In Extended Supergravity, Nucl. Phys. B 181 (1981) 487 [SPIRES].
11. R.E. Kallosh, Counterterms in extended supergravities, Phys. Lett. B 99 (1981) 122 [SPIRES].
12. P.S. Howe and K.S. Stelle, Supersymmetry counterterms revisited, Phys. Lett. B 554 (2003) 190 [hep-th/0211279] [SPIRES].
13. 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] [SPIRES].
14. K. Stelle, Supergravity: Finite after all?, Nature Phys. 3 (2007) 448.
15. G. Bossard, P.S. Howe and K.S. Stelle, The ultra-violet question in maximally supersymmetric field theories, Gen. Rel. Grav. 41 (2009) 919 [arXiv:0901.4661] [SPIRES].
16. 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] [SPIRES].
17. K.S. Stelle, Is N = 8 supergravity a finite field theory?, Fortsch. Phys. 57 (2009) 446 [SPIRES].
18. N. Berkovits, New higher-derivative R4 theorems, Phys. Rev. Lett. 98 (2007) 211601 [hep-th/0609006] [SPIRES].
19. 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] [SPIRES].
20. M.B. Green, J.G. Russo and P. Vanhove, Ultraviolet properties of maximal supergravity, Phys. Rev. Lett. 98 (2007) 131602 [hep-th/0611273] [SPIRES].
21. N. Berkovits, M.B. Green, J.G. Russo and P. Vanhove, Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory, JHEP 11 (2009) 063 [arXiv:0908.1923] [SPIRES].
22. M.B. Green, J.G. Russo and P. Vanhove, Automorphic properties of low energy string amplitudes in various dimensions, Phys. Rev. D 81 (2010) 086008 [arXiv:1001.2535] [SPIRES].
23. M.B. Green, J.G. Russo and P. Vanhove, String theory dualities and supergravity divergences, JHEP 06 (2010) 075 [arXiv:1002.3805] [SPIRES].
24. E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [SPIRES].
25. H. Elvang, D.Z. Freedman and M. Kiermaier, Solution to the Ward Identities for Superamplitudes, arXiv:0911.3169 [SPIRES].
26. N. Marcus, Composite Anomalies In Supergravity, Phys. Lett. B 157 (1985) 383 [SPIRES].
27. P. di Vecchia, S. Ferrara and L. Girardello, Anomalies Of Hidden Local Chiral Symmetries In σ-models And Extended Supergravities, Phys. Lett. B 151 (1985) 199 [SPIRES].
28. R. Kallosh, On UV properties of N = 8 Supergravity, Johns Hopkins Workshop "Maximal Supersymmetry", Gothenburg Sweden, 20 August 2009.
29. R. Kallosh, UV Properties of N=8 SG, Supergravity versus Superstring Theory in the Ultraviolet, Penn State U.S.A., 27-30 August 2009, http://www.gravity.psu.edu/events/supergravity/proceedings.shtml.
30. R. Kallosh, N = 8 Supergravity on the Light Cone, Phys. Rev. D 80 (2009) 105022 [arXiv:0903.4630] [SPIRES].
31. 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] [SPIRES].
32. D.J. Gross and E. Witten, Superstring Modifications of Einstein's Equations, Nucl. Phys. B 277 (1986) 1 [SPIRES].
33. D.J. Gross and J.H. Sloan, The Quartic Effective Action for the Heterotic String, Nucl. Phys. B 291 (1987) 41 [SPIRES].
34. S. Deser and D. Seminara, Tree amplitudes and two-loop counterterms in D = 11 supergravity, Phys. Rev. D 62 (2000) 084010 [hep-th/0002241] [SPIRES].
35. S. Stieberger, On tree-level higher order gravitational couplings in superstring theory, arXiv:0910.0180 [SPIRES].
36. R. Kallosh, On a possibility of a UV finite N = 8 supergravity, arXiv:0808.2310 [SPIRES].
37. 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] [SPIRES].
38. S. Deser, J.H. Kay and K.S. Stelle, Renormalizability Properties of Supergravity, Phys. Rev. Lett. 38 (1977) 527 [SPIRES].
39. R. Kallosh, C.H. Lee and T. Rube, N = 8 Supergravity 4-point Amplitudes, JHEP 02 (2009) 050 [arXiv:0811.3417] [SPIRES].
40. K. Risager, A direct proof of the CSW rules, JHEP 12 (2005) 003 [hep-th/0508206] [SPIRES].
41. H. Elvang, D.Z. Freedman and M. Kiermaier, Recursion Relations, Generating Functions and Unitarity Sums in N = 4 SYM Theory, JHEP 04 (2009) 009 [arXiv:0808.1720] [SPIRES].
42. H. Elvang, D.Z. Freedman and M. Kiermaier, Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory, JHEP 06 (2009) 068 [arXiv:0811.3624] [SPIRES].
43. F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [SPIRES].
44. M.B. Green, J.G. Russo and P. Vanhove, Low energy expansion of the four-particle genus-one amplitude in type-II superstring theory, JHEP 02 (2008) 020 [arXiv:0801.0322] [SPIRES].
45. M.B. Green, J.G. Russo and P. Vanhove, Modular properties of two-loop maximal supergravity and connections with string theory, JHEP 07 (2008) 126 [arXiv:0807.0389] [SPIRES].
46. H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [SPIRES].
47. G.'t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincare Phys. Theor. A 20 (1974) 69 [SPIRES].
48. M.T. Grisaru, P. van Nieuwenhuizen and J.A.M. Vermaseren, One Loop Renormalizability of Pure Supergravity and of Maxwell-Einstein Theory in Extended Supergravity, Phys. Rev. Lett. 37 (1976) 1662 [SPIRES].
49. M.T. Grisaru, Two Loop Renormalizability of Supergravity, Phys. Lett. B 66 (1977) 75 [SPIRES].
50. 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 [SPIRES].
51. R. Kallosh, On UV Finiteness of the Four Loop N = 8 Supergravity, JHEP 09 (2009) 116 [arXiv:0906.3495] [SPIRES].
52. P. Vanhove, private communication.
53. 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] [SPIRES].
54. E. Cremmer and B. Julia, The N = 8 Supergravity Theory. 1. The Lagrangian, Phys. Lett. B 80 (1978) 48 [SPIRES].
55. E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [SPIRES].
56. R. Kallosh and T. Kugo, The footprint of E7 in amplitudes of N = 8 supergravity, JHEP 01 (2009) 072 [arXiv:0811.3414] [SPIRES].
57. C. Cheung and D. O'Connell, Amplitudes and Spinor-Helicity in Six Dimensions, JHEP 07 (2009) 075 [arXiv:0902.0981] [SPIRES].
58. R. Boels, Covariant representation theory of the Poincaré algebra and some of its extensions, JHEP 01 (2010) 010 [arXiv:0908.0738] [SPIRES].