How can QED have degenerate vacua without superselection? This question is based on Andrew Strominger's lecture on the IR structure of field theories, in particular Section 2.11
The usual story with spontaneous symmetry breaking is as follows. You have degenerate vacua. In and of itself, that's not special, because in principle the system can tunnel from one to the other, so the true vacuum is a superposition of all of these. However, in a field theory, there's no finite energy process that can do that, so the tunnelling amplitude is zero. We say the vacua are not just degenerate, but also superselected. The Hilbert space decomposes, and you can't superpose states living in the different factors.
Now, it turns in QED, the large gauge transformations are spontaneously broken. You have different vacua, differing by soft photons. However, as Strominger says, creating soft photons is a perfectly valid process, so there's no superselection, and the Hilbert space doesn't decompose. So why isn't the true vacuum some superposition of all of them?
 A: Maybe this tentative answer is better than nothing, but I hope somebody else gives a better answer...
The context for Strominger's paper is scattering theory, focusing on past and future null infinity. Photons can reach from/to past/future null infinity, but massive particles only go from/to past/future timelike infinity. 
Consider this statement from the middle of page 38, the page that discusses the issue of SSB and superselection sectors:

The vacuum state is changed by soft photon creation, which occurs in nearly all scattering processes.

How can scattering occur in a vacuum state? Maybe the "vacuum state" wording here is referring to past/future null infinity, ignoring whatever goes from/to past/future timelike infinity. If so, then maybe all of the assertions about SSB and superselection sectors in that context need to be interpreted in some kind of "modulo massive particles" way. The next paragraph explains what I mean by this.
In QED, the absence of massive particles (from the state) implies the absence of charged particles, and in the absence of charged particles, soft photons are not created (assuming flat spacetime). Different Hilbert-space representations whose lowest-energy states involve different configurations of soft photons must belong to different superselection sectors (as Arnold Neumaier indicated in a comment), simply because a separable Hilbert space can't support a continuum of mutually-orthogonal states. However, if we pick one of those representations and consider a state with charged particles, then the configuration of soft photons can change with time. Maybe we can interpret Strominger's "vacuum state" language as referring exclusively to what happens at past/future null infinity (ignoring timelike infinity), and then his assertions are consistent with the usual picture of superselection sectors — just expressed in a modified language that refers to different null-infinity configurations as different "vacuum states," disregarding all the stuff that goes from/to past/future timelike infinity.
