Scattering amplitudes and BCFW recursion in twistor space
Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scatt...
| Main Authors: | , |
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| פורמט: | Journal article |
| שפה: | English |
| יצא לאור: |
2010
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| _version_ | 1826266341404835840 |
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| author | Mason, L Skinner, D |
| author_facet | Mason, L Skinner, D |
| author_sort | Mason, L |
| collection | OXFORD |
| description | Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for nparticle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N2MHV super-amplitude. We also give simple closed form formulae for the N = 8 supergravity recursion and the MHV and MHV̄ amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N kMHV, the amplitudes are given by 2n - 4 integrals in the form of Hilbert transforms of a product of n - k - 2 purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in N = 4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan. |
| first_indexed | 2024-03-06T20:37:26Z |
| format | Journal article |
| id | oxford-uuid:3318979b-f6c4-4562-84af-3c205b369448 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:37:26Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:3318979b-f6c4-4562-84af-3c205b3694482022-03-26T13:18:16ZScattering amplitudes and BCFW recursion in twistor spaceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3318979b-f6c4-4562-84af-3c205b369448EnglishSymplectic Elements at Oxford2010Mason, LSkinner, DTwistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for nparticle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N2MHV super-amplitude. We also give simple closed form formulae for the N = 8 supergravity recursion and the MHV and MHV̄ amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N kMHV, the amplitudes are given by 2n - 4 integrals in the form of Hilbert transforms of a product of n - k - 2 purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in N = 4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan. |
| spellingShingle | Mason, L Skinner, D Scattering amplitudes and BCFW recursion in twistor space |
| title | Scattering amplitudes and BCFW recursion in twistor space |
| title_full | Scattering amplitudes and BCFW recursion in twistor space |
| title_fullStr | Scattering amplitudes and BCFW recursion in twistor space |
| title_full_unstemmed | Scattering amplitudes and BCFW recursion in twistor space |
| title_short | Scattering amplitudes and BCFW recursion in twistor space |
| title_sort | scattering amplitudes and bcfw recursion in twistor space |
| work_keys_str_mv | AT masonl scatteringamplitudesandbcfwrecursionintwistorspace AT skinnerd scatteringamplitudesandbcfwrecursionintwistorspace |