Galois descent for real spectra

We prove analogs of faithfully flat descent and Galois descent for categories of modules over E-infinity-ring spectra using the infinity-categorical Barr-Beck theorem proved by Lurie. In particular, faithful G-Galois extensions are shown to be of effective descent for modules. Using this we study the category of ER(n)-modules, where ER(n) is the Z/2-fixed points under complex conjugation of a generalized Johnson-Wilson spectrum E(n). In particular, we show that ER(n)-modules is equivalent to Z/2-equivariant E(n)-modules as stable infinity-categories.