Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder

Understand

We compute the direct current resistivity of a scale-invariant, $d$-dimensional strange metal with dynamic critical exponent $z$ and hyperscaling-violating exponent $\theta$, weakly perturbed by a scalar operator coupled to random-field disorder that locally breaks a $\mathbb{Z}_2$ symmetry.

• Independent calculations via Einstein-Maxwell-Dilaton holography and memory matrix methods lead to the same results.
• We show that random field disorder has a strong effect on resistivity: charge carriers in the infrared are easily depleted, as the relaxation time for momentum is surprisingly small.
• In the course of our holographic calculation we use a non-trivial dilaton coupling to the disordered scalar, allowing us to study a strongly-coupled scale invariant theory with $\theta \ne 0$.