Gauge Theory Amplitudes from Cubic Scalar Feynman diagrams

TL;DR

The paper addresses the problem of organizing gauge-theory perturbative amplitudes by relating them to cubic scalar diagram integrands through Corolla differential operators, a connection previously highlighted by graph-homology insights. It shows that this transmutation emerges naturally from the field-theory limit of Witten's open string field theory, where the leading interactions are captured by Corolla differentials acting on scalar cubic diagrams. By detailing the construction of Corolla polynomials and their differential action, and by deriving the field-theory limit of open-string amplitudes, the authors derive gauge-theory integrands from scalar ones and connect Slavnov–Taylor identities to the Corolla framework. The results reveal a deep link between graph-homology and string field theory and hint at possible stringy generalizations that could inform Wilsonian effective actions. Overall, the work provides a rigorous bridge between cubic string field theory, Corolla differentials, and non-Abelian gauge amplitudes, with potential practical impact on systematic amplitude computations.

Abstract

Feynman diagrams are the foremost tool in the perturbative study of quantum field theory. In gauge theories, the full potential of this tool is revealed when it is combined with the Slavanov-Taylor identities associated with the local gauge symmetry. Hence, it is desirable to have perturbative expansion of scattering amplitudes that combine the graphical nature of Feynman diagram expansion and the reations among various diagrams due to the Slavanov-Taylor identities. In a remarkable paper, motivated by the similarity between graph homology and the gauge theory BRST homology, Kreimer, Sars and van Suijlekom found such an expansion. The implication of this expansion is that the amplitudes in a generic non-abelian gauge theory can be constructed by transmuting the renormalised integrands of trivalent Feynman diagrams in a scalar quantum field theory. In this paper, we show that this surprising connection naturally emerges from Witten's open string field theory in the field theory limit.