Abstract
We introduce a decomposition of $D$-dimensional vector amplitudes in terms of building blocks that preserve all partial amplitude relations of the parent gauge theory. Using this decomposition, we derive a new set of amplitude relations between nonlinear sigma model pions and the pure-scalar sector of Yang-Mills scalar theory. These new relations indicate an equivalence between Born-Infeld duality invariance and that of Einstein-Maxwell theory, considering their known double-copy construction from the two scalar theories with Yang-Mills. This observation motivates a general framework for constructing duality-invariant effective field theory observables at any multiplicity using the building blocks in our amplitude decomposition. Finally, we conjecture a subtle relationship between these duality-invariant building blocks and the bosonic sector of $\mathcal{N}=4$ super Yang-Mills.
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