Maldacena and Susskind proposed to identify ER (non-traversable wormholes i.e. Einstein-Rosen bridges) with EPR (entanglement). The former is a universal geometric visualization of the latter – which may become "simple" in special cases, just like in the case of a duality.
Just like you could expect even if you knew nothing about the content of ER=EPR, Vijay and pals offer a "double debunking" of the equivalence. They say that
- ER (wormhole) may exist even without large correlations/entanglement (EPR)
- EPR (high correlations) may exist even without ER (a wormhole)
Except that if I read the paper, I think that they only present two types of argumentation (I think that "arguments" is too strong a word) in favor of their second proposition – namely that the correlations may exist in contexts without a wormhole.
If I understand it well enough, the first argumentation claims that a smooth semiclassical wormhole implies large correlations but they can define complicated enough entangled states for which the double-sided correlators are tiny so they can't follow from a semiclassical wormhole.
In this part of their paper, I think that they are fighting a straw man. Maldacena and Susskind wouldn't claim that they have a simple, smooth, explicit wormhole description for a generic entangled state. In fact, you may find the word "generic" in a footnote which explicitly says that they are not making any statement about generic entangled states. They also say that various entangled states may be described by a wormhole that is not semiclassical at all – and whose topology depends on definitions in and subtleties of the Planckian regime of quantum gravity.
It seems to me that particular smooth, empty wormhole states connecting two wormholes are very special states in the Hilbert space of two black holes. However, their number may still be high enough to guarantee the smoothness of the interior i.e. to remove the firewall from a single black hole. However, Vijay et al. seem to be claiming that the generic entangled state of the two black holes aren't simple semiclassical states. I think that Maldacena and Susskind would agree and they have never claimed otherwise.
The second line of propositions that I see in Section 5 (page 18) argues that on the disconnected side of the Hawking-Page transition, they have two entangled thermal systems which are "manifestly without a Lorentzian wormhole". In this case, they are not fighting a straw man. That would indeed be a contradiction to ER=EPR except that their claim about the "manifest non-existence" of the wormhole doesn't seem to be justified by any evidence whatever. I think that ER=EPR manifestly implies that there is a wormhole connecting these two AdS spaces as well – the wormhole of some kind is a legitimate description of any entanglement.
Ironically enough, they seem to present evidence in favor of the geometric connection between the two AdS spaces: they are connected in the complexification of the spacetime where an Euclidean instanton linking them is located. Such a geometric connection visible in the Euclidean spacetime isn't the same thing as a simple connection in the Minkowski space but it is a geometric connection of a sort nevertheless. It would be very interesting to investigate what the character, shape, and excitation of the Lorentzian wormhole is when it's translated from the Euclidean picture. But they choose to flatly deny that there can be any wormhole at all. It seems to me that they have no evidence and one can't learn anything from this denial of theirs.
It's strange. I may be wrong but the paper looks like an example of the papers that argue against an important advance or insight in physics by simply assuming that everything that people have thought before this insight – including claims that have been proposed to be mistakes, for very clever, revolutionary reasons – has to be right and the development has to be denied because of that. No actual comparisons of evidence in favor of the "old picture" and the "new picture" is needed: the "new picture" is obliged to lose, they seem to suggest. Especially the claims about the "manifest non-existence of the wormhole" – when they manifestly seem to have no evidence whatever in favor of their absence – look like that.
There is such an increasing amount of cacophony and disagreements in the cutting-edge research of these general quantum gravity questions that I feel it must be pretty frustrating to communicate with generic researchers in the community.