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

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 ($++\dots +$) and next-to-self-dual ($-+\dots +$) 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.

arXiv comment52 pages

References in corpus (45)

• Dirichlet-Branes and Ramond-Ramond Charges
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics
• TASI Lectures on D-Branes
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Duality Symmetric Actions
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Massive Loop Amplitudes from Unitarity
• D-dimensional unitarity cut method
• Effective Field Theories from Soft Limits
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• On-Shell Recursion Relations for Effective Field Theories
• A Periodic Table of Effective Field Theories
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• D-branes and T-duality
• Basics of Generalized Unitarity
• Unifying Relations for Scattering Amplitudes
• Soft Bootstrap and Supersymmetry
• Loop amplitudes in gauge theories: modern analytic approaches
• Soft Photon and Graviton Theorems in Effective Field Theory
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams
• Vector Effective Field Theories from Soft Limits
• All-Multiplicity Amplitudes with Massive Scalars
• Recursion relations from soft theorems
• Scattering Amplitudes from Soft Theorems and Infrared Behavior
• Pions as Gluons in Higher Dimensions
• MHV, CSW and BCFW: field theory structures in string theory amplitudes
• SL(2,Z) duality of Born-Infeld theory from self-dual electrodynamics in 6 dimensions
• Soft Bootstrap and Effective Field Theories
• Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes
• The Infrared Structure of Nambu-Goldstone Bosons
• Uniqueness from gauge invariance and the Adler zero
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• M5-Brane and D-Brane Scattering Amplitudes
• On duality symmetry in perturbative quantum theory
• One-loop corrections to the D3 brane action
• Self-duality, helicity conservation and normal ordering in nonlinear QED
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• Helicity conservation in Born-Infeld theory

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