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This article covers the mathematical theory.
See also: Twister.
A time-slice (t=0) of a Robinson congruence.
The twistor theory, originally developed by Roger Penrose in 1967, is the mathematical theory which maps the geometric objects of the four dimensional space-time (Minkowski space) into the geometric objects in the 4-dimensional complex space with the metric signature (2,2).
The coordinates in such a space are called twistors.
For some time there was hope that the twistor theory may be the right approach towards solving quantum gravity, but this is now considered unlikely.
The twistor approach appears to be especially natural for solving the equations of motion of massless fields of arbitrary spin.
Recently, Edward Witten used twistor theory to understand certain Yang-Mills amplitudes, by relating them to a certain string theory, the topological B model, embedded in twistor space. This field has come to be known as twistor string theory.
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