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The temperature ($T$) and frequency ($\omega$) dependent conductivity ofweakly disordered Luttinger liquids is calculated in a systematic way both byperturbation theory and from a finite temperature renormalization group (RG)treatment to leading order in the disorder strength. Whereas perturbationtheory results in $\omega/T$ scaling of the conductivity such scaling isviolated in the RG traetment. We also determine the non-linear field dependenceof the conductivity, whose power law scaling is different from that oftemperature and frequency dependence.Comment: 4 pages, 4 figure

Frequency-temperature crossover in the conductivity of disordered Luttinger liquids