The Debye mass \(m_D\) (also \(m_E\)) is the inverse screening length of chromoelectric fields in a hot plasma of quarks and gluons. It is the strong-interaction analogue of Debye screening in an ordinary electromagnetic plasma, and in dimensional reduction it is the mass of the adjoint scalar \(A_0\) of EQCD.

A static color charge in the quark-gluon plasma does not produce an unscreened Coulomb field; instead the potential is Yukawa-screened,

\[ V(r)\ \sim\ \frac{e^{-m_D r}}{r}, \]

so electric interactions have finite range \(1/m_D\). This screening is why the temporal string tension vanishes above \(T_c\) — static charges are neutralized (deconfinement).

At high temperature, to leading order in the coupling,

\[ m_D^2 = \Big(\frac{N_c}{3}+\frac{N_f}{6}\Big)\,g^2(T)\,T^2 , \]

for [[non-abelian|SU\((N_c)\)]] with \(N_f\) fermion flavours. Parametrically \(m_D\sim gT\), i.e. the soft electric scale, sitting between the hard scale \(2\pi T\) and the ultrasoft magnetic scale \(g^2 T\).

• In EQCD, \(m_E=m_D\) is the mass term of the adjoint scalar \(A_0\).
• Because \(m_E\sim gT \gg g^2 T\), the field \(A_0\) is heavy on the magnetic scale and is integrated out, leaving MQCD.

There is no corresponding magnetic mass at leading order — the magnetic sector is unscreened and non-perturbative (the Linde problem) — which is precisely why the spatial string tension survives and must be computed in MQCD.