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
Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...
in 2003.
Twistor theory
In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should ...
was introduced by
Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...
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.
[Twistor theory and Scattering Amplitudes](_blank)
University of Oxford Mathematical Group. (retrieved 2 December 2015)
During this period,
Edward Witten
Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...
was a leading developer of
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
. 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
In mathematics, the Grassmannian \mathbf_k(V) (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all k-dimension (vector space), dimensional linear subspaces of an n-dimensional vector space V over a ...
residue formulae, the
amplituhedron and
holomorphic linking.
See also
*
BCFW recursion
The Britto–Cachazo–Feng–Witten recursion relations are a set of on-shell recursion relations in quantum field theory. They are named for their creators, Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten.
The BCFW recursion method i ...
*
MHV amplitudes
References
String theory
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