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In this paper the pure spinor formalism is used to obtain a compactexpression for the superstring N-point disk amplitude. The color ordered stringamplitude is given by a sum over (N-3)! super Yang-Mills subamplitudesmultiplied by multiple Gaussian hypergeometric functions. In order to obtainthis result, the cohomology structure of the pure spinor superspace isexploited to generalize the Berends-Giele method of computing super Yang-Millsamplitudes. The method was briefly presented in [1], and this paper elaborateson the details and contains higher-rank examples of building blocks andassociated cohomology objects. But the main achievement of this work is toidentify these field-theory structures in the pure spinor computation of thesuperstring amplitude. In particular, the associated set of basis worldsheetintegrals is constructively obtained here and thoroughly investigated togetherwith the structure and properties of the amplitude in [2].

Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation