Abstract: Understanding strong interactions at extreme densities has become important with the improved accuracy of observational neutron star physics. Unlike in the high-temperature-regime of collider physics, lattice simulations are not feasible at high densities due to the sign problem, leaving perturbation theory as one of the only first-principles methods for gaining insight on the inner workings of the cores of neutron stars.

I will start by discussing the general methodology of finite-density loop calculations and the modifications necessary compared to vacuum perturbation theory, , including the effective-field-theory framework necessary for properly treating the low-energy degrees of freedom. Following a general introduction, I will discuss the current state of the art for computing the perturbative equation of state at finite density, recently pushed to O(g^6 log g) accuracy. I will also briefly discuss how these calculations can be applied to transport phenomena, relevant for neutron star collisions, particularly focussing on the QCD input to the bulk viscosity of dense matter.