Light dark matter in NMSSM and non-diagonalization of BH evolution matrices

I want to mention two new papers today.

First, Jonathan Kozaczuk and Stefano Profumo of Santa Cruz discuss the possibility to embed the very light, sub-\(10\GeV\) dark matter particle (indicated by some of the direct search experiments) to the Next to Minimal Supersymmetric Standard Model (NMSSM: it's the MSSM in which the Higgs bilinear coefficient \(\mu\) is promoted a chiral superfield \(S\) which is, according to many criteria and physicists, more natural than the MSSM itself):

Light NMSSM Neutralino Dark Matter in the Wake of CDMS II and a \(126\GeV\) Higgs

They find out that there are regions in the parameter space of NMSSM that are able to produce this very light higgsino-singlino-mixed LSP dark matter candidate with a huge, spin-dependent cross section coupling it to the nucleons. The Higgs mass may be achieved sort of naturally, other "negative" constraints may also be satisfied, and the scenario produces some automatic predictions, e.g. a large invisible branching fraction of the Higgs decays.




Yesterday, I watched some black-hole-information talks in Santa Barbara, especially the whole talk by Suvrat Raju about his paper with Papadodimas. The talk was rather impressive, Suvrat (my former TA, I am tempted to proudly say, although his brilliance has nothing to do with your humble correspondent) was responding to a stream of questions and they addressed pretty much all the criticisms.




There is a new related paper by Steve Hsu today in which he reiterates and perhaps updates his February 2013 paper,

Factorization of unitarity and black hole firewalls (arXiv)

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Promotion of the paper on Steve's blog

I've left the following comment on Steve's blog:

Nice paper, I completely agree with you: all the potential final microstates are being mixed in the most general way so it's certainly incorrect to assume that the evaporating black hole Hilbert space may be rewritten as a direct sum of many "superselection sectors" that evolve unitarily and independently so that the evolution matrix would block-diagonalize in that splitting. This is one of the wrong assumptions constantly made by AMPS and followers - one that effectively amounts to believing that the geometry is purely classical and the gross features of a system like BH are perfectly predictable which they're not. Just to be sure, the evolution matrix may not only be block-diagonalized but diagonalized but its eigenstates are not states with a simple classical representation, e.g. a sharp center-of-mass location, they're not eigenstates of some natural local operators etc. They have no reason to be.

Also, just to sure, you're not the first one who pointed out pretty much the same thing but it's nice that you cite Nomura, Varela, Weinberg, and friends for whom this was a key point to point out. In fact, I think that the main "controversial" point of the Raju-Papadodimas paper (at least according to the structure of questions during Raju's Monday talk in Santa Barbara) - that the definition of the interior BH field operators in terms of the CFT operators is microstate-dependent - is pretty much equivalent to this your or Nomura gang's claim that the superselection sectors aren't separated (the evolution matrix isn't block-diagonalized in those subsets). The relevant subset of the Hilbert space to which one may "plausibly" evolve by a simple action of a few operators etc. depends on the ket vector we start with and the spacetime has no good reason to be a good "description of the background" if one deviates too much (by too many creation operators etc.), because of the back-reaction.

So in a "neighborhood" (in the sense of measuring the number of simple actions of natural operators) of a microstate, the local operators are sort of well-defined, but they become increasingly inadequate for more general, "faraway" microstates. This Papadodimas-Raju statement implicitly says that the definition of the local operators must gradually change as you change the microstates but there are no sharp borders between the neighborhoods, so no block-diagonal decomposition is possible. Instead, it's essential for the unitarity that all the microstates from the superselection sectors may be transformed to each other. The exponentially small matrix entries (including those between what AMPS and others would consider different superselection sectors) can't be neglected because they're essential even for the difference between pure density matrices and the maximally mixed one, see Papadodimas-Raju or

Hawking radiation: pure and mixed states are microns away

The microstate-dependence or the non-decoupling to the classical superselection sectors seems like a totally obvious point when looked at from a proper direction: it just means that the "Hilbert space of plausible pure states" and their organization that one needs to consider is allowed to depend on the rough or gross or "classical" evolution of the system: the Hilbert space of finely grained microstates is "fibered" over the space of coarse degrees of freedom and the character of the fiber may change. This is obvious - that's why we consider things like "the mass M black hole Hilbert space" at all (the spaces for different M are different; after all, they have different dimensions, even though both belong to a grander space of string theory) and why we can separate these states from others in the Hilbert space.

But the point is that the organization of the subspaces of the Hilbert space by local operators in the black hole interior is dependent not just on the presence of the black hole and its mass but "most" of its microstate details if a black hole is present. To me, this sounds sort of inevitable because one needs a "more than infinite" Schwarzschild time to penetrate inside the event horizon which means that in a certain Schwarzschild-time-slicing-based basis, a huge amount of scrambling that can mix really everything that waits to be mixed is performed on the local degrees of freedom right when an observer is crossing the horizon. There's absolutely no reason why the evolution operator should be block-diagonalized in the "superselection sectors" that look like classical patches. Superpositions of all of them may occur and therefore will occur.

I think that many of you are saying the same thing - or at least a big portion of what I consider the right answer to most of the questions here - but you don't fully appreciate that you use different words for the same insights.

Incidentally, Scott Aaronson who attended the KITP Santa Barbara fuzz-or-fire workshop posted a blog entries with some links and quotes about this topic.