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The gluon tree amplitudes of open twistor string theory, defined as contourintegrals over the ACCK link variables, are shown to satisfy the BCFWrelations, thus confirming that they coincide with the corresponding amplitudesin gauge field theory. In this approach, the integration contours are specifiedas encircling the zeros of certain constraint functions that force theappropriate relation between the link variables and the twistor stringworld-sheet variables. To do this, methods for calculating the tree amplitudesusing link variables are developed further including diagrammatic methods fororganizing and performing the calculations.

Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory