All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity

We initiate a study of non-supersymmetric Born-Infeld electrodynamics in 4d at the quantum level. Explicit all-multiplicity expressions are calculated for the purely rational one-loop amplitudes in the self-dual ($++\ldots+$) and next-to-self-dual ($-+\ldots+$) helicity sectors. Using a supersymmetric decomposition, $d$-dimensional unitarity cuts of the integrand factorize into tree-amplitudes in a 4d model of Born-Infeld photons coupled to a massive complex scalar. The two-scalar tree-amplitudes needed to construct the Born-Infeld integrand are computed using two complimentary approaches: (1) as a double-copy of Yang-Mills coupled to a massive adjoint scalar with a dimensionally reduced form of Chiral Perturbation Theory, and (2) by imposing consistency with low-energy theorems under a reduction from 4d to 3d and T-duality. The Born-Infeld integrand is integrated in $d=4-2\epsilon$ dimensions at order $\mathcal{O}(\epsilon^0)$ using the dimension-shifting formalism. We comment on the implications for electromagnetic duality in quantum Born-Infeld theory.