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The answer can be found in section 6 of http://www.sciencedirect.com/science/article/pii/0550321381902376. Above the Hagedorn temperature, the strong interaction becomes long-ranged and falls of as $1/r$, just like the Coulomb interaction. As you braid a charge-$e/3$ quark around a Dirac string, it picks up an Aharonov-Bohm phase from the quark's electric ...
This is fully contained in the paper, from understanding the sections that came before your statement. Namely: Section 5 of the paper studies QED using "perturbative expansion" which requires the charge $e$ of the electron to be small, and this is how the Higgs mechanism (with respect to electrons) occurs. From Dirac's quantization condition, the charge $q$...