Heterotic and bosonic string amplitudes via field theory

TL;DR

The paper expands the double-copy paradigm to bosonic and heterotic strings by identifying a tension-controlled, alpha'-dependent gauge theory based on dimension-six operators, paired with Z-theory-like disk/sphere integrals to reproduce massless tree amplitudes. In the open-string sector, the bosonic amplitudes arise from Z-theory ⊗ $(DF)^2$+YM, while closed-string amplitudes emerge from a corresponding double copy with single-valued projections; the heterotic string further employs a scalar-extended $(DF)^2$+YM+φ^3 theory, yielding a rich network of single- and multi-trace amplitudes and BCJ relations. In the alpha'-infinity limit, the framework connects to conformal gravity and related gauge–gravity theories, enabling new amplitude relations and CHY-inspired representations; the work also outlines explicit Lagrangians and partial amplitudes supporting these double-copy constructions and discusses future extensions to loops and broader dualities. Overall, the results reveal a universal field-theory underpinning for string amplitudes and illuminate deep links between string tension, higher-derivative gauge dynamics, and gravity via double-copy structures.

Abstract

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 $(D_μF^{μν})^2$, has previously appeared in the double-copy construction of conformal supergravity. We elaborate on the $α' \rightarrow \infty$ limit in this picture and derive new amplitude relations for various gauge-gravity theories from those of the heterotic string.