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

Journal of High Energy Physics, Sep 2017

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.

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Yusuke Sakata, Robin Schneider, Yuji Tachikawa, Takemasa Yamaura. On hydrogen-like bound states in $\mathcal{N}$ = 4 super Yang-Mills, Journal of High Energy Physics, 2017, 15, DOI: 10.1007/JHEP09(2017)015