One-loop Correlators and BCJ Numerators from Forward Limits

TL;DR

This work develops a unified forward-limit construction of one-loop ambitwistor-string correlators for gauge theories in even dimensions, yielding BCJ numerators with linearized loop propagators. Central innovations include new all-multiplicity tree-level two-fermion correlators, a spinor-to-vector trace conversion that exposes supersymmetry cancellations, and parity-odd completions from chiral fermions. The framework extends to general gauge theories in $D<10$ and provides compact BCJ numerators up to seven points via multiparticle fields, revealing power-counting structures and tensor decompositions in terms of the $t_8$-tensor and its multiparticle generalizations. These results enable efficient extraction of BCJ numerators from one-loop ambitwistor-string correlators and offer a clear path toward higher-loop extensions and deeper understanding of kinematic algebras in gauge theories.

Abstract

We present new formulas for one-loop ambitwistor-string correlators for gauge theories in any even dimension with arbitrary combinations of gauge bosons, fermions and scalars running in the loop. Our results are driven by new all-multiplicity expressions for tree-level two-fermion correlators in the RNS formalism that closely resemble the purely bosonic ones. After taking forward limits of tree-level correlators with an additional pair of fermions/bosons, one-loop correlators become combinations of Lorentz traces in vector and spinor representations. Identities between these two types of traces manifest all supersymmetry cancellations and the power counting of loop momentum. We also obtain parity-odd contributions from forward limits with chiral fermions. One-loop numerators satisfying the Bern-Carrasco-Johansson (BCJ) duality for diagrams with linearized propagators can be extracted from such correlators using the well-established tree-level techniques in Yang-Mills theory coupled to biadjoint scalars. Finally, we obtain streamlined expressions for BCJ numerators up to seven points using multiparticle fields.

Figures (1)

• Figure 1: Interpretation of the partial-fraction representation of loop integrals as $(n{+}2)$-point tree-level diagrams.