Gravitino Interactions from Yang-Mills Theory

TL;DR

This work extends KLT-based methods to gravitino interactions by deriving gravitino–graviton vertices from on-shell Yang-Mills amplitudes, yielding compact, factorized Feynman rules that are verified up to five-point scattering. A key result is the factorization of the gravitino three-point vertex into a gravitino–gluino–gluon piece and a gluon triple vertex, along with explicit gravitino contact terms and a leading-order Lagrangian. A subtraction scheme isolates contact contributions from KLT-constructed amplitudes, and higher-point checks (including two gravitinos and two gravitons, and a five-point four-gravitino one-graviton case) demonstrate consistency with traditional approaches. The findings suggest that KLT-inspired left–right decompositions organize interactions in a way that can simplify gravitino physics and potentially other matter sectors.

Abstract

We fabricate gravitino vertex interactions using as only input on-shell Yang-Mills amplitudes and the Kawai-Lewellen-Tye gauge theory / gravity relations. A useful result of this analysis is simpler tree-level Feynman rules for gravitino scattering than in traditional gauges. All results are explicitly verified until five point scattering.

Figures (10)

• Figure 1: Color-ordered Feynman rules for gluons and gluinos in Feynman gauge with all momenta out-going.
• Figure 2: Factorization of the gravitino three vertex.
• Figure 3: The scheme for obtaining the four vertex through the KLT relations.
• Figure 4: The factorization of the gravitino contact term.
• Figure 5: The four diagrams we need to compute the amplitude $\mathcal{M}_4(1^-_{\widetilde{h}},2^-_{h}, 3^+_{\widetilde{h}},4^+_{h})$.