Minimal Basis for Gauge Theory Amplitudes

TL;DR

The paper demonstrates that string-theory monodromy relations enforce a minimal basis of (n-3)! color-ordered gauge-theory amplitudes, and that these relations generalize the Kleiss-Kuijf relations to the full n-point case. By systematically exploiting contour deformations and the α'→0 limit, it connects all color orderings to a compact basis and recovers, in field theory, the Bern et al. conjecture on basis size. The KLT construction then expresses gravity amplitudes in a symmetric, left-right product form in terms of this gauge-theory basis, with explicit four- and five-point examples illustrating the structure. Overall, the work unifies gauge and gravity amplitudes through string-theoretic monodromy, providing both a minimal basis for gauge amplitudes and a constructive framework for gravity amplitudes in terms of open-string data.

Abstract

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.

Figures (5)

• Figure 1: Contour of integration for the amplitude $\mathcal{A}{(1,2,3,4)}$.
• Figure 2: Flipped contour for the amplitude $\mathcal{A}{(1,2,3,4)}$.
• Figure 3: Contour for the amplitude $\mathcal{A}(\beta_1,\ldots,\beta_r,1,\alpha_1,\dots,\alpha_s,n)$.
• Figure 4: Flipped contour of fig. \ref{['fig3']}.
• Figure 5: Integrals associated with the contours of fig. \ref{['fig4']}.