Twistor string theory - Misplaced Pages

Aspect of theoretical physics

String theory

Fundamental objects
String Cosmic string Brane D-brane
Perturbative theory
Bosonic Superstring (Type I, Type II, Heterotic)
Non-perturbative results
S-duality T-duality U-duality M-theory F-theory AdS/CFT correspondence
Phenomenology
Phenomenology Cosmology Landscape
Mathematics
Geometric Langlands correspondence Mirror symmetry Monstrous moonshine Vertex algebra K-theory
Related concepts Theory of everything Conformal field theory Quantum gravity Supersymmetry Supergravity Twistor string theory N = 4 supersymmetric Yang–Mills theory Kaluza–Klein theory Multiverse Holographic principle
Theorists Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Curtright Dijkgraaf Distler Douglas Duff Dvali Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey Hořava Horowitz Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind 't Hooft Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach
History Glossary
v t e

Twistor string theory is an equivalence between N = 4 supersymmetric Yang–Mills theory and the perturbative topological B model string theory in twistor space.

It was initially proposed by Edward Witten in 2003.

Twistor theory was introduced by Roger Penrose from the 1960s as a new approach to the unification of quantum theory with gravity. Twistor space is a three-dimensional complex projective space in which physical quantities appear as certain structural deformations. Spacetime and the familiar physical fields emerge as consequences of this description. But twistor space is chiral (handed) with left- and right-handed objects treated differently. For example, the graviton for gravity and the gluon for the strong force are both right-handed.

During this period, Edward Witten was a leading developer of string theory. In 2003, he produced a paper showing how string theory may be introduced into twistor space to provide a full physical model incorporating both left- and right-handed fields together with their full interactions.

The most important contribution of twistor string theory has been in the calculation of particle-particle collision scattering amplitudes, which determine the probabilities of the possible scattering processes. Witten showed that they have a remarkably simple structure in twistor space; in particular amplitudes are supported on algebraic curves. This has allowed both better understanding of experimental observations in particle colliders and deep insights into the natures of different quantum field theories. These insights have in turn led to new insights in pure mathematics. Such topics include Grassmannian residue formulae, the amplituhedron and holomorphic linking.

References

Witten, Edward (2004). "Perturbative Gauge Theory As A String Theory In Twistor Space". Communications in Mathematical Physics. 1. 252 (1): 189–258. arXiv:hep-th/0312171. Bibcode:2004CMaPh.252..189W. doi:10.1007/s00220-004-1187-3. S2CID 14300396.
^ Twistor theory and Scattering Amplitudes, University of Oxford Mathematical Group. (retrieved 2 December 2015)

Topics of twistor theory

Objectives

Principles	Background independence
Final objective	Quantum gravity Theory of everything

Mathematical concepts

Twistors	Penrose transform Twistor space

Physical concepts

Theories of gravitation

Standard

Newtonian gravity (NG)	Newton's law of universal gravitation Gauss's law for gravity Poisson's equation for gravity History of gravitational theory
General relativity (GR)	Introduction History Mathematics Exact solutions Resources Tests Post-Newtonian formalism Linearized gravity ADM formalism Gibbons–Hawking–York boundary term

Alternatives to
general relativity

Paradigms	Classical theories of gravitation Quantum gravity Theory of everything
Classical	Poincaré gauge theory Einstein–Cartan Teleparallelism Bimetric theories Gauge theory gravity Composite gravity f(R) gravity Infinite derivative gravity Massive gravity Modified Newtonian dynamics, MOND AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström Whitehead Geometrodynamics Induced gravity Degenerate Higher-Order Scalar-Tensor theories
Quantum-mechanical	Euclidean quantum gravity Canonical quantum gravity Wheeler–DeWitt equation Loop quantum gravity Spin foam Causal dynamical triangulation Asymptotic safety in quantum gravity Causal sets DGP model Rainbow gravity theory
Unified-field-theoric	Kaluza–Klein theory Supergravity
Unified-field-theoric and quantum-mechanical	Noncommutative geometry Semiclassical gravity Superfluid vacuum theory Logarithmic BEC vacuum String theory M-theory F-theory Heterotic string theory Type I string theory Type 0 string theory Bosonic string theory Type II string theory Little string theory Twistor theory Twistor string theory
Generalisations / extensions of GR	Liouville gravity Lovelock theory (2+1)-dimensional topological gravity Gauss–Bonnet gravity Jackiw–Teitelboim gravity

Pre-Newtonian
theories and
toy models

See also

References