On hydrogen-like bound states in $\mathcal{N}=4$ super Yang-Mills

Abstract

Using relativistic quantum mechanics, we study the spectrum of a non-BPS two-particle bound state in the massive phase of $\mathcal{N}=4$ super Yang-Mills, in the limit when one of the particles is infinitely heavier than the other. We find that the spectrum shows the exact $n^2$ degeneracy for each principal quantum number $n$, just as in the strict non-relativistic limit. This is in line with the findings of Caron-Huot and Henn, who studied the same system in the large $N$ limit with the technique of integrability and the dual conformal symmetry.

9 pages, 3 figures

References in corpus (6)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
• The static potential in {\cal N}=4 supersymmetric Yang-Mills at weak coupling
• From Six to Four and More: Massless and Massive Maximal Super Yang-Mills Amplitudes in 6d and 4d and their Hidden Symmetries