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Vafa and pals mass-produce swampland hypotheses

In 2005, Cumrun Vafa, a top topological string theorist and the father of F-theory (whose office was next to mine), not only knew that the sourballs claiming that "string theory didn't predict anything" were full of manure (he was using even more polite words than I do) but he was also capable of developing a repeatable framework to produce evidence that string theory predicts a lot, the swampland program.

While it looks like string theory may emulate basically "all effective (quantum) field theories coupled to gravity", with some discrete values of the parameters that are separated from each other by some spacing, in reality, it's probably not true. String theory implies that an overwhelming majority of effective field theories coupled to gravity are inconsistent at the level of quantum gravity – they cannot be completed to consistent theories of quantum gravity (or identified as approximate descriptions of some stringy vacua) – because they violate certain general principles, rules that are somewhat analogous to the uncertainty principle in quantum mechanics.

These sick effective field theories are said to be in the "swampland". We really want to study the nice "landscape" which obeys the criteria – in this sense, the "swampland" terminology is an inverse or negative one.



That visionary paper has over 350 citations by now but it is a visionary one, and therefore somewhat sketchy and not filled with too much very detailed, quantitative, tangible evidence involving non-trivial mathematics (but the paper is much more than some philosophy!). A followup of ours, the Weak Gravity Conjecture (WGC), is a narrower hypothesis that has about 550 followups by now – and in this sense, it's more well-known than the whole swampland program where it belongs.



But the swampland program is so much more than the WGC and Cumrun, along with various co-authors, has formulated many conjectures about the "surprising, purely stringy consequences" that string theory actually implies or predicts although these predictions look unexpected from the viewpoint of effective field theories. Many of these "siblings of the WGC" are various inequalities that ban the large-field inflation, de Sitter spaces in string theory, long-lived metastable de Sitter spaces, and more. Some of these conjectures and proposed no-go theorems were linked to some older hypotheses including Penrose's Cosmic Censorship Conjecture and others (that "censorship" word will appear below, too).

If true, some of Cumrun's papers contain partial evidence of the possible fact that the huge ensembles of the KKLT de Sitter vacua – exploited in the landscape project and eternal inflation – actually don't exist in string theory when that theory is studied precisely. Instead, they are just misleading artifacts of the "effective field theory" approximation.

Especially in recent months, Cumrun apparently accelerated the rate at which he is proposing these rules, see his publication list sorted from the newest additions. He's released the third September 2019 hep-th paper today, quite a pace. One is about vortices and the \(G_2\) holonomy and seems unrelated to the swampland.

Yesterday, along with Jacob McNamara, Vafa banned non-trivial cobordism classes in the stringy configuration space. I was primarily exposed to the word "cobordism" during a course by Greg Moore at Rutgers – so I would mostly be able to reconstruct the definition. OK, cobordism is a relationship between two manifolds that may be interpolated in between through a higher-dimensional manifold (with one more dimension). But I am clearly not thinking in terms of such words which are too mathematical.

There's another reason – besides the opposition to the overly mathematical "cobordism" jargon – which makes me feel uncomfortable. And the reason is that there is really nothing such as the "configuration space of fields in string theory" simply because string theory isn't really a quantization of a classical field theory, at least not one with finitely many fields. For this reason, I believe that string theory forces us to use a more physical language. When translated to the physics language, Cumrun and McNamara basically say that there shouldn't exist certain finite-energy domain walls in string theory. That ban – they mansplain – is mostly equivalent to a special kind of a ban on the global symmetries in string theory.

It's very interesting, there's some partial evidence – but I think that there's also some intuition, Cumrun's black magic, and I think that he's among the people in the world who have the highest chance to guess similar correct relationships just by exploiting his intuition. Intuition and black magic sound supernatural – but at the end, what he is doing is a mental activity combining seemingly diverse and unrelated facts into generalized or otherwise new ones. Some people could do a "superficially equivalent" black magic but when two men are doing the same thing, it is not the same thing, and whether you believe me or not, I have reasons to think that Vafa's guesses are far more likely to be right than "seemingly similar" guesses by almost all other people.

Today, along with Alek Bedroya, Vafa proposed another swampland conjecture, the Trans-Planckian Censorship Conjecture. This hypothesis is clearly different from Penrose's Cosmic Censorship Conjecture – but it shows how Penrose has influenced the choice of the words by physicists who want to propose new restrictions and no-go-like principles in physics. They claim that the Planckian quantum fluctuations are never allowed to grow to trans-Hubble, cosmological scales (i.e. a particular nice story from the popular books that the CMB patterns show the quantum fluctuations that were stretched to cosmological scales must be ultimately wrong if they are right) – which primarily has the effect of banning long-lived metastable de Sitter spaces. They write the formula for the maximum allowed life time of a de Sitter space in string theory – it must be short-lived so that "to think about it as a de Sitter space" is basically useless and impossible. As you can see, Cumrun doesn't really believe the most standard story about the cosmic inflation.

(Tomorrow, Vafa and Bedroya will add two new authors and publish another paper about TCC which will primarily conclude that the primordial gravitational waves have to have a negligible amplitude if they're right.)

On one hand, one could argue that these papers reflect some "bias" – he and co-authors may be said to be rationalizing some pre-existing irrational inflation-phobia (not to be confused with Islamophobia). On the other hand, it is very clear that the phobia isn't quite irrational and because of the partial evidence and the general overrepresentation of no-go theorems in physics, combined with Vafa's good track record in the intuition, there exists a genuine possibility that these far-reaching no-go theorems are true – and perhaps ultimately provable by a straightforward proof, using the so far unknown definition of string theory, just like the Heisenberg's uncertainty relationships are provable by a triangle inequality applied to the Hilbert spaces.

By now, there exists quite an elaborate network of restrictions and conditions that may follow from string theory as understood properly – and that is alternative in the sense that a "majority of the string phenomenologists and cosmologists believe in things that contradict almost everything in this Vafa's network of rules". Who is right? This question is mostly equivalent to a simpler question "how much new and original string theory is relatively to the effective field theory framework that approximates it at long distances?". If string theory is sufficiently new and different, then the swampland conditions of Vafa's type are probably true, at least some of them. If string theory is "just" a new parameterization of the effective field theories coupled to gravity, one that doesn't change things qualitatively, but one with some actual but not too interesting quantization conditions for the parameters, then Vafa and co-authors are probably wrong.

It's great to build the network of the possible swampland wisdom. But it's still annoying that we're so utterly uncertain about their validity. It would be great if we made more progress in rigorously proving them (OK, I know that numerous papers actually presented some of these apparently complete proofs but there's still something that is missing). Some of them might be proven by thoughts based on the "experimental thinking about physics" combined with the effective field theory framework. But maybe for the more general swampland conditions, one needs a new, more universal definition of string theory that is not available as of now – or at least we don't appreciate such a definition if it is available.

It would be cute if someone suddenly brought us a 5-line proof – analogous to the proof of the Heisenberg uncertainty inequalities – which would imply that the long-lived de Sitter spaces are banned or other things are true or false. Before such a thing happens, we will probably have to live with this fundamental uncertainty about the compatibility of string theory with the large field inflation, cosmic inflation in general, with the multiverse-based "explanations" for the fine-tuned fundamental parameters, and with many other things. We understand the string vacua with the unbroken supersymmetry rather well but when it comes to the truly realistic configurations in string theory, ones with broken SUSY etc., our certainty about the calculations that we have remains limited.

This uncertainty about these basic questions is a huge opportunity for a truly breathtaking scientific advance – that could be made e.g. by a very young researcher. Too bad that many such potential discoverers are told to skip the classes and wave their parade sticks on Fridays and to believe that the physicist's task is to "fill the time" instead of working hard on these damn important and exciting fundamental physics questions.

And that's the memo.

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