Heterotic and bosonic string amplitudes via field theory

Previous work has shown that massless tree amplitudes of the type I and IIA/B superstrings can be dramatically simplified by expressing them as double copies between field-theory amplitudes and scalar disk/sphere integrals, the latter containing all the α′-corrections. In this work, we pinpoint similar double-copy constructions for the heterotic and bosonic string theories using an α′-dependent field theory and the same disk/sphere integrals. Surprisingly, this field theory, built out of dimension-six operators such as (DμFμν)2, has previously appeared in the double-copy construction of conformal supergravity. We elaborate on the α′ → ∞ limit in this picture and derive new amplitude relations for various gauge-gravity theories from those of the heterotic string.