Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory

TY - JOUR

T1 - Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory

AU - Caron-Huot, Simon

AU - Henn, Johannes M.

PY - 2014/10/16

Y1 - 2014/10/16

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.113.161601

DO - 10.1103/PhysRevLett.113.161601

M3 - Journal article

SN - 0031-9007

VL - 113

JO - Physical Review Letters

JF - Physical Review Letters

IS - 16

M1 - 161601

ER -