2014/08/31 by Simon Caron-Huot, Johannes M. Henn
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Mathematical physics #Particle physics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevlett.113.161601
published as Phys. Rev. Lett. 113, 161601 (2014) · 4 pages, 3 figures. Clarifications added; published version
openalex publication_date 2014/10/16 · arxiv created 2015/01/16 · arxiv updated 2015/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N = 4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling.