Spin-spin and spin-orbit interactions in strongly coupled gauge theories

We evaluate the spin-orbit and spin-spin interactions between two fermions in strongly coupled gauge theories in their Coulomb phase. We use the quasi-instantaneous character of Coulomb's law at strong coupling to resum a class of ladder diagrams. For N = 4 SYM we derive both weak and strong coupling limits of the spin-orbit and spin-spin interactions, and find that in the latter case these interactions are subleading corrections and do not seriously affect the deeply bound Coulomb states with large angular momentum, pointed out in our previous paper. The results are important for understanding of the regime of intermediate coupling, which is the case for QCD somewhat above the chiral transition temperature.