descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Mar 2016Embargo end date: 01 Jan 2015 English Publisher:Springer Science and Business Media LLCJournal:Journal of High Energy Physics, volume 2,016 (eissn: 1029-8479,

Authors: Colwell, Kitran; Terning, John;

doi: 10.1007/jhep03(2016)068 , 10.48550/arxiv.1510.07627

arXiv: 1510.07627

S-duality and helicity amplitudes

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Abstract

We examine interacting Abelian theories at low energies and show that holomorphically normalized photon helicity amplitudes transform into dual amplitudes under SL(2,Z) as modular forms with weights that depend on the number of positive and negative helicity photons and on the number of internal photon lines. Moreover, canonically normalized helicity amplitudes transform by a phase, so that even though the amplitudes are not duality invariant, their squares are duality invariant. We explicitly verify the duality transformation at one loop by comparing the amplitudes in the case of an electron and the dyon that is its SL(2,Z) image, and extend the invariance of squared amplitudes order by order in perturbation theory. We demonstrate that S-duality is property of all low-energy effective Abelian theories with electric and/or magnetic charges and see how the duality generically breaks down at high energies.

27 pages, 3 figures

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Keywords

High Energy Physics - Theory, Nuclear and High Energy Physics, Particle and Plasma Physics (for), FOS: Physical sciences, Effective field theories, 5106 Nuclear and plasma physics (for-2020), Atomic, 530, Mathematical Sciences, Particle and Plasma Physics, High Energy Physics - Phenomenology (hep-ph), 4902 Mathematical physics (for-2020), 0105 Mathematical Physics (for), Nuclear, 5107 Particle and high energy physics (for-2020), Scattering Amplitudes, Mathematical Physics, 5107 Particle and High Energy Physics (for-2020), Quantum Physics, 51 Physical Sciences (for-2020), Molecular, Nuclear & Particles Physics (science-metrix), Particle and High Energy Physics, 0206 Quantum Physics (for), Solitons Monopoles and Instantons, Nuclear & Particles Physics, Nuclear and plasma physics, High Energy Physics - Phenomenology, High Energy Physics - Theory (hep-th), Physical Sciences, 0202 Atomic, 4902 Mathematical Physics (for-2020), 49 Mathematical Sciences (for-2020), Duality in Gauge Field Theories

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