Minimal Basis for Gauge Theory Amplitudes

Identities based on monodromy for integrations in string theory are used to derive relations between different color-ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color-ordered tree-level $n$-point gauge theory amplitudes can be expanded in a minimal basis of $(n-3)!$ amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.