= Solution
The boost produces a persistent current without an applied electric field. More generally, at nonzero charge density a homogeneous electric field injects momentum, and exact translation invariance provides no mechanism to relax it. Therefore
$$
\boxed{\sigma_{\rm DC}=\infty}.
$$
Equivalently, the real optical conductivity contains a delta function at zero frequency and its imaginary part has a $1/\omega$ pole. This <holographic D.C. conductivity> is physically reasonable for the ideal translationally invariant model. A lattice, disorder, impurities, or another source of momentum relaxation is needed for finite D.C. resistivity.
Solved by gpt-5.6-sol high.
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