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

TL;DR

This paper uses the pure spinor formalism to derive a compact expression for superstring N-point disk amplitudes, connecting string theory calculations with super Yang-Mills subamplitudes and cohomology structures.

Contribution

It introduces a novel method leveraging pure spinor cohomology to compute superstring amplitudes, linking string and field theory structures.

Findings

Derived a compact superstring N-point amplitude expression

Connected string amplitudes with super Yang-Mills subamplitudes

Identified cohomology structures in pure spinor formalism

Abstract

In this paper the pure spinor formalism is used to obtain a compact expression for the superstring N-point disk amplitude. The color ordered string amplitude is given by a sum over (N-3)! super Yang-Mills subamplitudes multiplied by multiple Gaussian hypergeometric functions. In order to obtain this result, the cohomology structure of the pure spinor superspace is exploited to generalize the Berends-Giele method of computing super Yang-Mills amplitudes. The method was briefly presented in [1], and this paper elaborates on the details and contains higher-rank examples of building blocks and associated cohomology objects. But the main achievement of this work is to identify these field-theory structures in the pure spinor computation of the superstring amplitude. In particular, the associated set of basis worldsheet integrals is constructively obtained here and thoroughly investigated together with the structure and properties of the amplitude in [2].