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Twistor theory at fifty: from contour integrals to twistor strings
Michael Atiyah1,2, Maciej Dunajski3, Lionel J Mason4
1School of Mathematics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|November 10, 2017
Summary
Twistor theory redefines spacetime, deriving events from holomorphic curves. This approach encodes solutions to physics equations, yielding instantons and integrable systems, and offers new methods for quantum scattering amplitudes.
Area of Science:
- Theoretical Physics
- Mathematical Physics
- String Theory
Background:
- Twistor theory offers an alternative framework to spacetime.
- It views spacetime events as derived objects linked to holomorphic curves.
Purpose of the Study:
- To review five decades of twistor theory's aims and achievements.
- To demonstrate its application in solving mathematical physics equations.
- To explore its role in quantum gravity and scattering amplitudes.
Main Methods:
- Elementary construction of twistor space.
- Encoding solutions of anti-self-duality equations into twistor cohomology.
- Reviewing Yang-Mills and gravitational instantons.
- Examining reductions of anti-self-dual equations for integrability.
- Exploring holomorphic string theories in twistor spaces.
Main Results:
- Explicit examples of Yang-Mills and gravitational instantons.
- Underlying framework for solitonic and Einstein-Weyl systems.
- New formulae for quantum scattering amplitudes.
- Connection to the Newtonian limit and quantum gravity.
Conclusions:
- Twistor theory provides a powerful framework for understanding fundamental physics.
- It unifies diverse areas from instantons to quantum scattering.
- It offers potential insights into quantum gravity and wave function collapse.
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