Electromagnetic Duality and D3-Brane Scattering Amplitudes Beyond Leading Order

Abstract

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for $n$-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in $\epsilon$, expression for the 1-loop integrand of the MHV sector of $\mathcal{N}=4$ DBI. (4) For all $n>4$, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in $\mathcal{N}=4$ DBI) are shown to be removable at $\mathcal{O}({\epsilon }^0)$ by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

arXiv comment59 pages, minor revisions

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• Off-Shell Color-Kinematics Duality for Chern-Simons
• Generalizations of the Double-Copy: the KLT Bootstrap
• Virtues of a symmetric-structure double copy
• Multi-spin soft bootstrap and scalar-vector Galileon
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• The seeds of EFT double copy