title: Solvable relativistic hydrogenlike system in supersymmetric Yang-Mills theory.
abstract: 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.
authors.affiliation: Niels Bohr International Academy and Discovery Center, Blegdamsvej 17, Copenhagen 2100, Denmark and Institute for Advanced Study, Princeton, New Jersey 08540, USA.
authors.forename: Simon
authors.initials: S
authors.lastname: Caron-Huot
authors.affiliation: Institute for Advanced Study, Princeton, New Jersey 08540, USA.
authors.forename: Johannes M
authors.initials: JM
authors.lastname: Henn