Cumrun Vafa's swampland paradigm is the assumption that the apparent consistency conditions of low-energy effective field theory are just a small portion of the conditions that are required for the spectrum and interactions of a theory to be compatible with quantum gravity. Matter coupled to quantum gravity (e.g. string theory which may be a synonym) is far more constrained and far more unique than the low-energy optics suggests.
In 1978, in order to earn a demijohn of slivovitz, Ivan Mládek composed this song, Joey the Swampthing, which was my #1 favorite song in the kindergarten years (and I have won many contests by singing it LOL). In recent years, every ambitious band has to perform this song (here is Metallica's attempt). As this English translation shows, the song has successfully predicted the rise and fall of Joe Biden.
The swampland program is the plan to maximally isolate these extra conditions that are invisible to the effective field theory and perhaps use this extra information to map the string landscape – and to help to find the right vacuum describing this particular Universe. The string landscape is large but the point is that the space of the effective field theories is much larger and its anti-string portion (the swampland) that is incompatible with the swampland conditions must be drained. The draining led by Vafa will continue at least up to January 20th, 2021 when the swampland creatures may take over the U.S. again. Incidentally, I think that Vafa still doesn't realize how important Trump has been for Vafa's program to drain the swamp. Nobody is perfect.
Over 500 papers have been written about the swampland program. Well, this 500 should include the 750 papers on the weak gravity conjecture. The violation of the apparently crucial inequality occurs because many weak gravity researchers don't realize that it is a part of the "swampland thinking" or they don't care about the latter. Today, two new papers were added to the swampland research.
Markus Dierigl and Jonathan J. Heckman (Jonathan has been an important collaborator of Vafa's for some time, it was interesting to watch them) wrote the following:
McNamara swampland conjecture saying that the "the bordism group of quantum gravity is trivial". A bordism is a relationship between two manifolds – basically saying that one may interpret them as two similar boundaries of a higher-dimensional manifold that "interpolates between them". In practice, the requirement that "the bordism group must be trivial" implies the existence of extra objects similar to domain walls that may change "the vacuum of one type to another". Note that this swampland principle relates "the spectrum of objects" (those that interpolate) and "the set of would-be vacua or stationary points in the moduli space" – these two categories of concepts are pretty much independent in an effective field theory. That's a reason to say that the swampland program achieves a "deeper unification of the fundamental concepts of physics".
D7-branes are codimension-two branes in type IIB string theory (which has 12 spacetime dimensions but 2 of them are demanded to be compactified to a Planckian torus). Their existence may be derived from the requirement "the bordism group is trivial". However, a funny fact about type IIB string theory is that it has the S-duality group \(SL(2,\ZZ)\) – which comes from the maps acting on the two-torus (two tiny compactified dimensions of the 12D spacetime) – and as you can see, this group is non-Abelian. The spectrum of 7-branes in type IIB string theory is larger than the minimum spectrum implied by "the bordism group is trivial".
OK, they realize that the larger spectrum of 7-branes exists because the extra information is remembered in the trajectories on the space of 2-tori. And when two of the 10 large dimensions of the type IIB spacetime are compactified on a sphere of a sort (with 7-branes adding to the total, predetermined deficit angle), these trajectories may be used to study how 7-branes create knots. They combine two swampland conjectures, Ooguri-Vafa and McNamara-Vafa, and conclude that only some congruence subgroups \(\Gamma\subseteq SL(2,\ZZ)\) may appear in the genus zero modular curves in 8D F-theory vacua. In this way, the whole known spectrum of allowed Mordell-Weiss torsion groups in 8D F-theory vacua, whatever they precisely are, is completely reproduced and derived from the swampland conditions and nothing else!
Swampland conditions really seem like "powerful underlying principles", perhaps analogous to the uncertainty principle and the postulates of relativity (and the equivalence principle). They are enough to derive many things if not all things about theories of quantum gravity. "What they exactly are" remains a bit misunderstood and fragmented but maybe on a sunny day in the future, all the swampland conditions will merge into a giant one.
In the other swampland paper,
These authors derive that assuming these required "small enough moduli spaces", the amount of non-geodesicity on the trajectories (some curvature or acceleration along the paths, pretty much a generalized force) is also bounded from above. A surprising consequence is that this maximum geodesicity is saturated in a class of flux vacua that is close to the KKLT, the model used to build the huge string landscape by the anthropic believers.
You see that in good physics, tools are ultimately more powerful than prejudices. Vafa has found a great new strategy to study string theory and the debunking of the "huge anthropic landscape" of flux vacua may have been one of his motivations. But the swampland program may ultimately lead to a legitimization of these flux vacua instead. Because they exactly saturate a bound on the geodesicity, their existence and "naturalness from the string theory viewpoint" looks more plausible than previously thought. These authors also argue that the SDC could allow itself to be circumvented by designing a procedure to UV-complete any moduli space in the broader class.