Title: Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals

Abstract: Luttinger semimetals represent materials with strong spin-orbit coupling, harbouring doubly degenerate quadratic band touchings at the Brillouin zone center. In the presence of Coulomb interactions, such a system exhibits a non-Fermi liquid phase [dubbed as the Luttinger-Abrikosov-Beneslavskii (LAB) phase], at low temperatures and zero doping. However, a clear experimental evidence of this emergent state remains elusive to this date. Here, we determine the Raman response of the LAB phase. At frequencies much larger than the temperature, the Raman response exhibits a power-law behavior, which could be verified experimentally. On the other hand, at lower frequencies, the Raman response displays a quasi-elastic peak. We also compute the ratio of the shear viscosity and the entropy density $\eta/s$, using a Kubo formula analysis, to analyze the consequences of the hyperscaling violation that emerges in the LAB phase.