Unraveling Ln,k: Grassmannian kinematics

Journal of High Energy Physics

Volumn 2010, Issue 3, 2010, Pages

  Kaplan, Jared ^a  

^a SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

Author keywords

1 N Expansion; Duality in gauge field theories; Extended supersymmetry

Indexed keywords

EID: 84856401173     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP03(2010)025     Document Type: Article

References (88)

1. N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, arXiv:0907.5418 [SPIRES].
2. F. Cachazo, Sharpening the leading singularity, arXiv:0803.1988 [SPIRES].
3. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, arXiv:0808.1446 [SPIRES].
4. Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to five gluon amplitudes, Phys. Rev. Lett. 70 (1993) 2677 [hep-ph/9302280] [SPIRES].
5. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One-loop n-point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [SPIRES].
6. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [SPIRES].
7. Z. Bern, V. Del Duca, L.J. Dixon and D.A. Kosower, All non-maximally-helicity-violating one-loop seven-gluon amplitudes in N = 4 super-Yang-Mills theory, Phys. Rev. D 71 (2005) 045006 [hep-th/0410224] [SPIRES].
8. Z. Bern, L.J. Dixon and D.A. Kosower, All next-to-maximally helicity-violating one-loop gluon amplitudes in N = 4 super-Yang-Mills theory, Phys. Rev. D 72 (2005) 045014 [hep-th/0412210] [SPIRES].
9. F. Cachazo, M. Spradlin and A. Volovich, Leading singularities of the two-loop six-particle MHV amplitude, Phys. Rev. D 78 (2008) 105022 [arXiv:0805.4832] [SPIRES].
10. M. Spradlin, A. Volovich and C. Wen, Three-loop leading singularities and BDS ansatz for five particles, Phys. Rev. D 78 (2008) 085025 [arXiv:0808.1054] [SPIRES].
11. Z. Bern, M. Czakon, D.A. Kosower, R. Roiban and V.A. Smirnov, Two-loop iteration of five-point N = 4 super-Yang-Mills amplitudes, Phys. Rev. Lett. 97 (2006) 181601 [hep-th/0604074] [SPIRES].
12. Z. Bern et al., The two-loop Six-Gluon MHV amplitude in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465] [SPIRES].
13. A.P. Hodges, Twistor diagram recursion for all gauge-theoretic tree amplitudes, hep-th/0503060 [SPIRES].
14. A.P. Hodges, Twistor diagrams for all tree amplitudes in gauge theory: a helicity-independent formalism, hep-th/0512336 [SPIRES].
15. A.P. Hodges, Scattering amplitudes for eight gauge fields, hep-th/0603101 [SPIRES].
16. N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-matrix in twistor space, arXiv:0903.2110 [SPIRES].
17. L. Mason and D. Skinner, Scattering amplitudes and BCFW recursion in twistor space, arXiv:0903.2083 [SPIRES].
18. G.P. Korchemsky and E. Sokatchev, Twistor transform of all tree amplitudes in N = 4 SYM theory, Nucl. Phys. B 829 (2010) 478 [arXiv:0907.4107] [SPIRES].
19. R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [SPIRES].
20. 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] [SPIRES].
21. N. Arkani-Hamed and J. Kaplan, On tree amplitudes in gauge theory and gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [SPIRES].
22. P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming tree amplitudes in general relativity, JHEP 11 (2007) 057 [hep-th/0702032] [SPIRES].
23. C. Cheung, On-shell recursion relations for generic theories, arXiv:0808.0504 [SPIRES].
24. J. Bedford, A. Brandhuber, B.J. Spence and G. Travaglini, A recursion relation for gravity amplitudes, Nucl. Phys. B 721 (2005) 98 [hep-th/0502146] [SPIRES].
25. F. Cachazo and P. Svrček, Tree level recursion relations in general relativity, hep-th/0502160 [SPIRES].
26. J.M. Drummond and J.M. Henn, All tree-level amplitudes in N = 4 SYM, JHEP 04 (2009) 018 [arXiv:0808.2475] [SPIRES].
27. R. Penrose, Twistor algebra, J. Math. Phys. 8 (1967) 345.
28. R. Penrose, Twistor quantization and curved space-time, Int. J. Theor. Phys., 1 (1968) 61.
29. R. Penrose and M.A.H. MacCallum, Twistor theory: an approach to the quantization of fields and space-time, Phys. Rept. 6 (1972) 241.
30. R. Penrose, The central programme of twistor theory, Chaos Solitons Fractals, 10 (1999) 581.
31. E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [SPIRES].
32. N. Arkani-Hamed, F. Cachazo and C. Cheung, The grassmannian origin of dual superconformal invariance, arXiv:0909.0483 [SPIRES].
33. L. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and grassmannians, JHEP 11 (2009) 045 [arXiv:0909.0250] [SPIRES].
34. L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [SPIRES].
35. J.M. Drummond, G.P. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [SPIRES].
36. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [SPIRES].
37. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys. B 826 (2010) 337 [arXiv:0712.1223] [SPIRES].
38. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude, Phys. Lett. B 662 (2008) 456 [arXiv:0712.4138] [SPIRES].
39. J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys. B 815 (2009) 142 [arXiv:0803.1466] [SPIRES].
40. 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] [SPIRES].
41. A. Brandhuber, P. Heslop and G. Travaglini, A note on dual superconformal symmetry of the N = 4 super Yang-Mills S-matrix, Phys. Rev. D 78 (2008) 125005 [arXiv:0807.4097] [SPIRES].
42. J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [SPIRES].
43. J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [SPIRES].
44. A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in N = 4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [SPIRES].
45. N. Berkovits and J. Maldacena, Fermionic T-duality, dual superconformal symmetry and the amplitude/Wilson loop connection, JHEP 09 (2008) 062 [arXiv:0807.3196] [SPIRES].
46. 5 superstring integrability, Phys. Rev. D 78 (2008) 126004 [arXiv:0807.3228] [SPIRES].
47. J. McGreevy and A. Sever, Planar scattering amplitudes from Wilson loops, JHEP 08 (2008) 078 [arXiv:0806.0668] [SPIRES].
48. - annihilation, Phys. Rev. D 46 (1992) 1980 [SPIRES].
49. Z. Kunszt, A. Signer and Z. Trócsányi, Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross-sections of multiparton processes, Nucl. Phys. B 420 (1994) 550 [hep-ph/9401294] [SPIRES].
50. L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359 [SPIRES].
51. S.J. Parke and T.R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56 (1986) 2459 [SPIRES].
52. V.P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B 214 (1988) 215 [SPIRES].
53. A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [SPIRES].
54. G.P. Korchemsky and E. Sokatchev, Symmetries and analytic properties of scattering amplitudes in N = 4 SYM theory, arXiv:0906.1737 [SPIRES].
55. R. Roiban, M. Spradlin and A. Volovich, Dissolving N = 4 loop amplitudes into QCD tree amplitudes, Phys. Rev. Lett. 94 (2005) 102002 [hep-th/0412265] [SPIRES].
56. R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [SPIRES].
57. P. Griffiths and J. Harris, Principles of algebraic geometry, John Wiley & Sons Inc, U.S.A. (1994).
58. A. Tsikh, Multidimensional residues and their applications, American Mathematical Society volume103, Reading U.S.A. (1992).
59. I.A. Aizenberg and A.P. Yuzhakov, Integral representations and residues in multidimensional complex analysis, Translations of Mathematical Monographs, American Mathematical Society volume58, Reading U.S.A. (1983).
60. N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, unpublished.
61. D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [SPIRES].
62. N. Beisert, C. Kristjansen and M. Staudacher, The dilatation operator of N = 4 super Yang-Mills theory, Nucl. Phys. B 664 (2003) 131 [hep-th/0303060] [SPIRES].
63. T. Bargheer, N. Beisert, W. Galleas, F. Loebbert and T. McLoughlin, Exacting N = 4 superconformal symmetry, JHEP 11 (2009) 056 [arXiv:0905.3738] [SPIRES].
64. E. Cremmer and B. Julia, The N = 8 supergravity theory. 1. The lagrangian, Phys. Lett. B 80 (1978) 48 [SPIRES].
65. E. Cremmer, B. Julia, and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B 76 (1978) 409 [SPIRES].
66. E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [SPIRES].
67. 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].
68. 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] [SPIRES].
69. 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] [SPIRES].
70. N.E.J. Bjerrum-Bohr, D.C. Dunbar and H. Ita, Six-point one-loop N = 8 supergravity NMHV amplitudes and their IR behaviour, Phys. Lett. B 621 (2005) 183 [hep-th/0503102] [SPIRES].
71. 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].
72. Z. Bern, L.J. Dixon and R. Roiban, Is N = 8 supergravity ultraviolet finite?, Phys. Lett. B 644 (2007) 265 [hep-th/0611086] [SPIRES].
73. 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].
74. 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].
75. N.E.J. Bjerrum-Bohr and P. Vanhove, Absence of triangles in maximal supergravity amplitudes, JHEP 10 (2008) 006 [arXiv:0805.3682] [SPIRES].
76. N.E.J. Bjerrum-Bohr and P. Vanhove, On cancellations of ultraviolet divergences in supergravity amplitudes, Fortsch. Phys. 56 (2008) 824 [arXiv:0806.1726] [SPIRES].
77. 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].
78. 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].
79. 4 theorems, Phys. Rev. Lett. 98 (2007) 211601 [hep-th/0609006] [SPIRES].
80. M.B. Green, J.G. Russo and P. Vanhove, Ultraviolet properties of maximal supergravity, Phys. Rev. Lett. 98 (2007) 131602 [hep-th/0611273] [SPIRES].
81. Z. Bern et al., Three-loop superfiniteness of N = 8 supergravity, Phys. Rev. Lett. 98 (2007) 161303 [hep-th/0702112] [SPIRES].
82. R. Kallosh, The effective action of N = 8 supergravity, arXiv:0711.2108 [SPIRES].
83. R. Kallosh, On a possibility of a UV finite N = 8 supergravity, arXiv:0808.2310 [SPIRES].
84. R. Kallosh, C.H. Lee and T. Rube, N = 8 supergravity 4-point amplitudes, JHEP 02 (2009) 050 [arXiv:0811.3417] [SPIRES].
85. Z. Bern, J.J.M. Carrasco and H. Johansson, Progress on ultraviolet finiteness of supergravity, arXiv:0902.3765 [SPIRES].
86. 7 in amplitudes of N = 8 supergravity, JHEP 01 (2009) 072 [arXiv:0811.3414] [SPIRES].
87. 7(7) on N = 8 supergravity fields, Nucl. Phys. B 801 (2008) 25 [arXiv:0802.4106] [SPIRES].
88. M. Bullimore, L. Mason and D. Skinner, Twistor-strings, grassmannians and leading singularities, arXiv:0912.0539 [SPIRES].