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F-theory with non-small Hodge numbers predicts a rich dark sector or a new stabilization mechanism

Mirjam Cvětičová plus Halverson, Lin, and Long (Slovenia+UPenn, CERN, Northeastern, Cornell) managed to post the first hep-th paper during the earliest possible second, like so many papers did before. I would be interested in their algorithm to adjust the timing of pressing "enter" at the sub-second precision. Surely this technology has made progress in recent 20 years. Do they connect the "enter" key to atomic clocks? ;-)

Constraints on Standard Model Constructions in F-theory
They prove that at least one of the following statements must be true in F-theory models:
  1. The Hodge number \(h^{1,1}\) is really small (not moderate or large)
  2. A new stabilization mechanism outside the supergravity approximation, i.e. outside LVS-or-KKLT-like calculations, is employed
  3. A new dark sector of particles attached to 7-branes is predicted
They have some rather specific F-theory models in mind, many of which have \(h^{1,1}=35\) (from a polytope) which is counted as a "moderately" large value.

OK, they consider some compactification using the tools of SUGRA, need to cancel a tadpole, get some high enough contribution related to seven-branes, and the Standard Model and/or new dark sectors are shown to exist simultaneously at prime toric and/or square-free divisors. They discuss some examples of geometry and also try to derive the statistical distribution of the Standard Model couplings.



There seems to be a trade-off (or a principle analogous to the uncertainty principle): if you confine the Standard Model onto a small divisor, a large dark sector pops out elsewhere.

While the math is abstract and advanced, they are really close to experimental physicists and discuss very particular types of geometries much of the time.



Let me just make it clear that I personally find the violation (1) most intriguing. For decades, I have believed – but it is still faith to some extent – that Nature favors the compactifications with the minimal or near-minimal possible values of the Hodge numbers. The violation of the SUGRA approximation is something that I also tend to expect. People make things "easy", namely accessible to \(\alpha'\)-expansions and supergravity, because they want to have clear well-defined results in a finite amount of time.

But Nature can get harder results equally easily so She is not constrained by this bias – which I consider mostly anthropocentric. So She can favor strong-coupling-based stabilization that is extremely hard to calculate by existing (or all mathematically possible) approximation schemes. The relevant tools to accurately calculate such strong-coupled stabilization results are probably inaccessible even in principle right now.

And there can be a rich dark sector, too.

At some level, the demonstrated result, if true, isn't a "no-go theorem" that would kill a majority of options. But from a sociological viewpoint, I think that the paper is important because a substantial number of people – perhaps the Stanford-centered string cosmologists – would tend to believe that all these three simplifying conditions are satisfied simultaneously. Cvetič et al. have hopefully shown that these simplifying conditions can't hold simultaneously.

I must mention a more general point along these lines. The model building is still sufficiently "unsettled" so that people make "many more than one" simplifying assumptions that cannot really be demonstrated to be true. If the number of such assumptions is "much more than one", it becomes very likely that at least one of them fails. And in this particular case, it was indeed shown that at least one has to fail. Nature may be "close to minimal" in many respects but She is probably not "quite minimal in all respects" that people decided to demand.

You may want to make things as simple as possible but not more so.

And that's the memo.

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