String theory and the mapping of gravity into gauge theory

TL;DR

This work uses the Kawai–Llewellyn-Tye relations to relate gravity and Yang–Mills theories at the level of effective actions by matching on-shell tree amplitudes. By constructing field-redefinition–invariant effective Lagrangians for gravity and YM and applying KLT factorization, it derives explicit mappings between gravity and YM operators up to $O(\alpha'^2)$ and shows how certain gravitational invariants correspond to products of YM operators. The derived relations constrain the YM and gravity coefficients, revealing a Broader solution space than traditional string solutions and suggesting that KLT-type mappings can illuminate nontrivial connections between gauge and gravitational dynamics. The results point to a structured, higher-derivative correspondence and potential extensions to include matter and heterotic-like constructions.

Abstract

The relationship between on-shell tree level scattering amplitudes of open and closed strings, discovered some time ago by Kawai, Lewellen and Tye, is used at field theory level (at $O(α'^3)$) to establish a link between the general relativity and the non-abelian Yang-Mills effective actions. Insisting at the effective Lagrangian level that any tree $N$ point gravity on-shell scattering amplitude is directly factorisable into a sum of $N$ point left-right products of non-abelian Yang-Mills tree on-shell scattering amplitudes, non-trivial mappings of the effective general relativity operators into the effective non-abelian Yang-Mills operators are derived. Implications of such mapping relations of the field operators are discussed.