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 n2 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.