String amplitudes and twistor diagrams: an analogy

A proposal has been made for a conformal field theory in four dimensions (CFT4), in which the twistor representation of quantum fields plays an essential role. According to this proposal, a scattering amplitude could arise in the first instance as associated with a specific complex manifold X (bearing a specified relationship to flat twistor space); to obtain a physically meaningful amplitude a summation of these amplitudes would be performed over (a class of) such manifolds. It was noted that physically meaningful amplitudes (for theories of interacting massless fields in Minkowski space-time) have already appeared in twistor theory. They have arisen in the formalism of twistor diagrams - compact contour integrals in products of twistor spaces, with a rough analogy to Feynman diagrams, but with certain features similar to the dual diagrams of bosonic string theory. It was therefore suggested that there might exist a direct connection between the CFT4 picture and the twistor diagram formalism. This speculation is here strengthened by noting an analogy between standard two-dimensional string theory and a specific twistor-diagrammatic calculation, suggesting that the integration of twistor diagrams could be interpreted as a summation over complex manifolds. (author)