Proof of Gravity and Yang-Mills Amplitude Relations

TL;DR

The paper provides a field-theory proof, via BCFW on-shell recursion and BCJ relations, of a broad family of Kawai–Lewellen–Tye (KLT) relations that express tree-level gravity amplitudes as products of Yang–Mills amplitudes. Central to the construction are the BCJ-encoded S- and dual S-functions, which reorganize permutations and cancel spurious poles to yield gravity amplitudes from gauge-theory data. The authors derive multiple equivalent KLT forms with distinct permutation symmetries, including both $(n-3)!$ and $(n-2)!$ structures, and prove their equivalence through BCJ relations. The work solidifies a purely field-theoretic route to gravity amplitudes, clarifies the role of BCJ relations in KLT factorization, and points to future directions such as loop extensions and string-theory connections.

Abstract

Using BCFW on-shell recursion techniques, we prove a sequence of explicit n-point Kawai-Lewellen-Tye relations between gravity and Yang-Mills amplitudes at tree level.