Abstract
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 (+ + … +) and next-to-self-dual (− + … +) 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 − 2ϵ dimensions at order mathcal{O}left({in}^0right) using the dimension-shifting formalism. We comment on the implications for electromagnetic duality in quantum Born-Infeld theory.
Highlights
Proven to be a truly exceptional example of a low-energy effective theory of non-linear electrodynamics, though perhaps at times a mysterious one
We initiate a study of non-supersymmetric Born-Infeld electrodynamics in 4d at the quantum level
We comment on the implications for electromagnetic duality in quantum Born-Infeld theory
Summary
Our goal in this paper is to calculate SD and NSD one-loop amplitudes in nonsupersymmetric Born-Infeld in d = 4. We use d-dimensional generalized unitarity methods [13] to construct the complete loop-integrand in a physically motivated dimensional scheme. We begin with a brief overview of unitarity methods and describe in detail the approach taken in this paper.
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