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 -