Twistor theory at fifty: from contour integrals to twistor strings
We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary constru...
| Autores principales: | , , |
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| Formato: | Journal article |
| Publicado: |
Royal Society
2017
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| _version_ | 1826305587136167936 |
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| author | Atiyah, MF Dunajski, M Mason, LJ |
| author_facet | Atiyah, MF Dunajski, M Mason, LJ |
| author_sort | Atiyah, MF |
| collection | OXFORD |
| description | We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics—anti-self-duality equations on Yang–Mills or conformal curvature—can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang–Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang–Mills equations, and Einstein–Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function. |
| first_indexed | 2024-03-07T06:35:05Z |
| format | Journal article |
| id | oxford-uuid:f756d5eb-ea5d-4416-a43c-d895ff7ceefd |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:35:05Z |
| publishDate | 2017 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:f756d5eb-ea5d-4416-a43c-d895ff7ceefd2022-03-27T12:41:57ZTwistor theory at fifty: from contour integrals to twistor stringsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f756d5eb-ea5d-4416-a43c-d895ff7ceefdSymplectic Elements at OxfordRoyal Society2017Atiyah, MFDunajski, MMason, LJWe review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics—anti-self-duality equations on Yang–Mills or conformal curvature—can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang–Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang–Mills equations, and Einstein–Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function. |
| spellingShingle | Atiyah, MF Dunajski, M Mason, LJ Twistor theory at fifty: from contour integrals to twistor strings |
| title | Twistor theory at fifty: from contour integrals to twistor strings |
| title_full | Twistor theory at fifty: from contour integrals to twistor strings |
| title_fullStr | Twistor theory at fifty: from contour integrals to twistor strings |
| title_full_unstemmed | Twistor theory at fifty: from contour integrals to twistor strings |
| title_short | Twistor theory at fifty: from contour integrals to twistor strings |
| title_sort | twistor theory at fifty from contour integrals to twistor strings |
| work_keys_str_mv | AT atiyahmf twistortheoryatfiftyfromcontourintegralstotwistorstrings AT dunajskim twistortheoryatfiftyfromcontourintegralstotwistorstrings AT masonlj twistortheoryatfiftyfromcontourintegralstotwistorstrings |