Spin-Spin and Spin-Orbit Interactions in Strongly Coupled Gauge Theories

TL;DR

This paper investigates spin-dependent interactions between fermions in strongly coupled gauge theories, deriving limits for ${ m f N}=4$ SYM and discussing implications for QCD near the chiral transition.

Contribution

It provides a detailed analysis of spin-orbit and spin-spin interactions at strong coupling, including derivations for ${ m f N}=4$ SYM and insights into intermediate coupling regimes.

Findings

Spin-orbit and spin-spin interactions are subleading at strong coupling in ${ m f N}=4$ SYM.

These interactions do not significantly alter deeply bound Coulomb states with large angular momentum.

Results are relevant for understanding QCD near the chiral transition temperature.

Abstract

We evaluate the spin-orbit and spin-spin interaction 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 ${\cal N}=4$ SYM we derive both weak and strong coupling limits of the 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.