What is the current status of the swampland? Have people expanded the list of swampland criteria?

If let's say I wish to figure out if the Standard Model belongs to the swampland, are there any concrete steps I can use to go about it, at least in principle? If let's say technical difficulties aren't an objection, and we have access to a supercomputer with top notch programmers and mathematics code, is there any algorithmic procedure to show whether or not the Standard Model belongs to the swampland?


Yoshiko, the Standard Model belongs to the swampland for some easy reasons - you don't need a supercomputer for that. First of all, you should add gravity to the Standard Model - in some approximate way that people would normally do.

When you add gravity, the Standard Model still belongs to the swampland.

For example, it predicts that there are no magnetic monopoles. That's forbidden in the "landscape" of consistent theories of quantum gravity because one may demonstrate that pairs of black holes that carry the magnetic monopole charge may be pair-produced because of an instanton that enables this process.

There are probably many other pathological properties of the Standard Model that guarantee it is in the swampland but the map of all the conditions remains poorly understood. Let me just mention another example: the Standard Model perturbatively conserves the lepton and baryon charges. In the allowed theories of quantum gravity, there can't exist exact global symmetries (which don't produce any new local fields) and the baryon and lepton charges would violate this rule.

Of course, if you generalized the term "Standard Model" and included all theories that look like the Standard Model but may be modified at the GUT scale or another high energy scale (e.g. GUT theories themselves where magnetic monopoles can be easily constructed; and electroweak instantons allow one to violate at least $B$ or $L$ separately), then you would have to conclude that the generalized Standard Model almost certainly belongs to the "landscape" and is allowed.

After all, quantum gravity has to describe the real world. However, there are no rigorous ways to mathematically prove such a modest proposition at this moment. What is available at this moment are various constraints that may show that various theories are bad and belong to the swampland. One of those that were studied in recent years is the condition that "gravity has to be the weakest force".


Of course, the known conditions are useful to eliminate various pathological "cousins" of the Standard Model. The Standard Model itself is close to the actual laws of Nature so it doesn't suffer from "unfixable" pathologies - only from pathologies that arise from the incompleteness of the Standard Model.


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