String theory and the mapping of gravity into gauge theory

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.