In theoretical and mathematical physics, twistor theory is a theory proposed by Roger Penrose in 1967, as a possible path to a theory of quantum gravity.
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In twistor theory, the Penrose transform maps Minkowski space into twistor space, taking the geometric objects from a 4-dimensional space with a Hermitian form of signature (2,2) to geometric objects in twistor space, specified by complex coordinates are called twistors. The twistor approach is especially natural for solving the equations of motion of massless fields of arbitrary spin.
Background
Penrose's twistor theory is unique to four-dimensional Minkowski space, with its signature (3,1) metric. At the heart of twistor theory lies the isomorphism between the conformal group Spin(4,2) and SU(2,2), which is the group of unitary transformations of determinant 1 over a four-dimensional complex vector space that leave invariant a Hermitian form of signature (2,2), see classical group.
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Supertwistors
Supertwistors are a supersymmetric extension of twistors introduced by Alan Ferber in 1978. Along with the standard twistor degrees of freedom, a supertwistor contains N fermionic scalars, where N is the number of supersymmetries. The superconformal algebra can be realized on supertwistor space.
Twistor string theory
Twistor theory progressed slowly, in part because of mathematical challenges. Twistor theory also seemed unrelated to ideas in mainstream physics. While twistor theory appeared to say something about quantum gravity, its potential contributions to understanding the other fundamental interactions and particle physics were less obvious.
In 2003, Edward Witten proposed uniting twistor and string theory by embedding the topological B model of string theory in twistor space, whose dimensionality is necessarily the same as that of 3+1 Minkowski spacetime. His objective was to model certain Yang–Mills amplitudes.
The resulting model, defined on the supertwistor space
Penrose himself rejects string theory, and criticizes it in his book, Fashion, Faith, and Fantasy in the New Physics of the Universe.