Multi-loop amplitudes in maximally supersymmetric pure spinor field theory

Journal of High Energy Physics

Volumn 2011, Issue 1, 2011, Pages

  Björnsson, Jonas ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Extended supersymmetry; Field theories in higher dimensions; Supergravity models

Indexed keywords

EID: 80053118721     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP01(2011)002     Document Type: Article

References (67)

1. 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.
2. 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].
3. Z. Bern et al., Three-loop superfiniteness of N = 8 supergravity, Phys. Rev. Lett. 98 (2007) 161303 [hep-th/0702112].
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].
5. J. Björnsson and M. B. Green, 5 loops in 24/5 dimensions, JHEP 08 (2010) 132 [arXiv:1004.2692].
6. N. Berkovits, Super-Poincaré covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035].
7. N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120].
8. Z. Bern, J. S. Rozowsky and B. Yan, Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills, Phys. Lett. B 401 (1997) 273 [hep-ph/9702424].
9. L. Dixon, Multi-loop amplitudes with maximal supersymmetry, talk given at the meeting International workshop on gauge and string amplitudes, IPPP, Durham U. K. March 30-April 3 2009.
10. Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson and R. Roiban, The complete four-loop four-point amplitude in N = 4 super-Yang-Mills theory, arXiv:1008.3327.
11. P. S. Howe and U. Lindström, Higher order invariants in extended supergravity, Nucl. Phys. B 181 (1981) 487.
12. N. Berkovits, Superstring multiloop amplitudes and non-renormalization theorems - lecture I, lecture at the Spring School on Superstring Theory and Related Topics, International Centre for Theoretical Physics, Trieste Italy March 22-30 2010.
13. N. Berkovits, Superstring multiloop amplitudes and non-renormalization theorems - lecture II, lecture at the Spring School on Superstring Theory and Related Topics, International Centre for Theoretical Physics, Trieste Italy March 22-30 2010.
14. N. Berkovits, Superstring multiloop amplitudes and non-renormalization theorems - lecture III, lecture at the Spring School on Superstring Theory and Related Topics, International Centre for Theoretical Physics, Trieste Italy March 22-30 2010.
15. N. Berkovits, Superstring multiloop amplitudes and non-renormalization theorems - lecture IV, lecture at the Spring School on Superstring Theory and Related Topics, International Centre for Theoretical Physics, Trieste Italy March 22-30 2010.
16. P. Vanhove, The critical ultraviolet behaviour of N = 8 supergravity amplitudes, arXiv:1004.1392.
17. M. B. Green, J. G. Russo and P. Vanhove, String theory dualities and supergravity divergences, JHEP 06 (2010) 075 [arXiv:1002.3805].
18. 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].
19. H. Elvang, D. Z. Freedman and M. Kiermaier, A simple approach to counterterms in N = 8 supergravity, JHEP 11 (2010) 016 [arXiv:1003.5018].
20. 7(7) violation, JHEP 10 (2010) 108 [arXiv:1007.4813].
21. J. M. Drummond, P. J. Heslop and P. S. Howe, A note on N = 8 counterterms, arXiv:1008.4939.
22. G. Bossard, P. S. Howe and K. S. Stelle, On duality symmetries of supergravity invariants, arXiv:1009.0743.
23. 7(7) constraints on counterterms in N = 8 supergravity, Phys. Lett. B 694 (2010) 265 [arXiv:1009.1643].
24. P. Dai and W. Siegel, Worldline green functions for arbitrary Feynman diagrams, Nucl. Phys. B 770 (2007) 107 [hep-th/0608062].
25. N. Berkovits and C. R. Mafra, Equivalence of two-loop superstring amplitudes in the pure spinor and RNS formalisms, Phys. Rev. Lett. 96 (2006) 011602 [hep-th/0509234].
26. C. R. Mafra, Pure spinor superspace identities for massless four-point kinematic factors, JHEP 04 (2008) 093 [arXiv:0801.0580].
27. N. Berkovits, Super-Poincaré covariant two-loop superstring amplitudes, JHEP 01 (2006) 005 [hep-th/0503197].
28. C. R. Mafra, Superstring scattering amplitudes with the pure spinor formalism, arXiv:0902.1552.
29. N. Berkovits and C. R. Mafra, Some superstring amplitude computations with the non-minimal pure spinor formalism, JHEP 11 (2006) 079 [hep-th/0607187].
30. 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].
31. N. E. J. Bjerrum-Bohr and P. Vanhove, Explicit cancellation of triangles in one-loop gravity amplitudes, JHEP 04 (2008) 065 [arXiv:0802.0868].
32. N. E. J. Bjerrum-Bohr and P. Vanhove, Absence of triangles in maximal supergravity amplitudes, JHEP 10 (2008) 006 [arXiv:0805.3682].
33. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446].
34. E. P. Verlinde and H. L. Verlinde, Chiral bosonization, determinants and the string partition function, Nucl. Phys. B 288 (1987) 357.
35. E. D'Hoker and D. H. Phong, The geometry of string perturbation theory, Rev. Mod. Phys. 60 (1988) 917.
36. N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 09 (2001) 016 [hep-th/0105050].
37. M. Cederwall, private communication, (2010).
38. O. Chandía, The b ghost of the pure spinor formalism is nilpotent, arXiv:1008.1778.
39. U. Gran, GAMMA: a Mathematica package for performing G-matrix algebra and Fierz transformations in arbitrary dimensions, hep-th/0105086.
40. N. Berkovits and P. S. Howe, Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring, Nucl. Phys. B 635 (2002) 75 [hep-th/0112160].
41. P. A. Grassi and L. Tamassia, Vertex operators for closed superstrings, JHEP 07 (2004) 071 [hep-th/0405072].
42. L. Anguelova, P. A. Grassi and P. Vanhove, Covariant one-loop amplitudes in D = 11, Nucl. Phys. B 702 (2004) 269 [hep-th/0408171].
43. M. B. Green and J. H. Schwarz, Superstring interactions, Nucl. Phys. B 218 (1983) 43.
44. 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.
45. 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].
46. Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476].
47. Z. Bern, J. J. M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993].
48. M. Cederwall, Towards a manifestly supersymmetric action for 11-dimensional supergravity, JHEP 01 (2010) 117 [arXiv:0912.1814].
49. M. Cederwall, D = 11 supergravity with manifest supersymmetry, Mod. Phys. Lett. A 25 (2010) 3201 [arXiv:1001.0112].
50. N. Berkovits and N. Nekrasov, Multiloop superstring amplitudes from non-minimal pure spinor formalism, JHEP 12 (2006) 029 [hep-th/0609012].
51. Y. Aisaka and N. Berkovits, Pure spinor vertex operators in Siegel gauge and loop amplitude regularization, JHEP 07 (2009) 062 [arXiv:0903.3443].
52. P. A. Grassi and P. Vanhove, Higher-loop amplitudes in the non-minimal pure spinor formalism, JHEP 05 (2009) 089 [arXiv:0903.3903].
53. N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, JHEP 09 (2004) 047 [hep-th/0406055].
54. N. Berkovits and S. A. Cherkis, Pure spinors are higher-dimensional twistors, JHEP 12 (2004) 049 [hep-th/0409243].
55. S. Mandelstam, Light cone superspace and the ultraviolet finiteness of the N = 4 model, Nucl. Phys. B 213 (1983) 149.
56. L. Brink, O. Lindgren and B. E. W. Nilsson, The ultraviolet finiteness of the N = 4 Yang-Mills theory, Phys. Lett. B 123 (1983) 323.
57. 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].
58. H. Gomez, One-loop superstring amplitude from integrals on pure spinors space, JHEP 12 (2009) 034 [arXiv:0910.3405].
59. 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].
60. H. Gomez and C. R. Mafra, The overall coefficient of the two-loop superstring amplitude using pure spinors, JHEP 05 (2010) 017 [arXiv:1003.0678].
61. E. D'Hoker, M. Gutperle and D. H. Phong, Two-loop superstrings and S-duality, Nucl. Phys. B 722 (2005) 81 [hep-th/0503180].
62. 4 theorems, Phys. Rev. Lett. 98 (2007) 211601 [hep-th/0609006].
63. M. B. Green and M. Gutperle, Effects of D-instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093].
64. M. B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59 (1999) 046006 [hep-th/9808061].
65. M. B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027].
66. Z. Bern, T. Dennen, Y.-T. Huang and M. Kiermaier, Gravity as the square of gauge theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693].
67. M. Cederwall, Supergravity with pure spinors, talk given at the meeting International Conference on Strings, M-theory and Quantum Gravity, Monte Verita, Ascona Switzerland, July 25-30 2010.