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Vafa, quintessence vs Gross, Silverstein

It has been one year since Strings 2017 ended in the Israeli capital (yes, I mean Jerusalem, that's where Czechia has the honorary consulate) and Strings 2018 in Okinawa (list of titles) is here.

The Japanese organizers have tried an original reform of the YouTube activity. They post the whole days as unified videos.

Most of you want to delay your dinner by 3 hours and 46 minutes – so you should watch the video above for the food to taste better.

Cumrun Vafa whom I know much better than the other 20 speakers in the video starts to speak at 31:44 and his topic is a paper released on Monday,

De Sitter Space and the Swampland (Obied, Ooguri, Spodyneiko, Vafa)
Recall that Vafa's Swampland is a giant parameter space of effective field theories that cannot be realized within a consistent theory of quantum gravity i.e. within string/M-theory. Only a tiny island inside this Swampland, namely the stringy Landscape, is compatible with quantum gravity. String/M-theory makes lots of very strong predictions – namely that we don't live in the Swampland. We have to live in the special hospitable Landscape.

Along with his friend Donald Trump, Cumrun Vafa decided to drain the Swampland. ;-)

OK, these comments became ludicrous too early so let us be more serious for a while. In the paper I mentioned, Vafa and pals have proposed a new inequality obeyed by the potential energy \(V\) in every consistent theory of quantum gravity\[

V \leq \frac{|\nabla V|}{c}

\] which excludes too high positive cosmological constants and de Sitter spaces in particular. The gradient is calculated on the field space, with the metric given by the kinetic terms of the scalar fields. Use 4D Planck units (Einstein frame) if others aren't good enough.

It's a fun proposal – a potential cousin of the Weak Gravity Conjecture, but a younger and less justified one (at least so far). Note that \(V_0\leq 0\) constraining the minimum would be hard to justify and the appearance of the minimum \(V_0\) only would be unnatural. So in a sense, Vafa and co-authors have found and supported a stronger version of that inequality that places an upper bound on the potential energy density at each point of the configuration space. Neat.

For a while after I saw the paper, I was worried about the infinite tower of massive stringy fields which make the gradient arbitrarily high – because the mass is high. But then I understood my mistake. If the vacua are stabilized, the gradient from the inequality by Vafa et al. is strictly zero and they make the bold statement that the cosmological constant in stable vacua has to be zero (Minkowski) or negative (AdS).

I think it's a cool inequality and people should investigate the arguments for and against and the consequences. Such a simple inequality could indeed summarize the absence of persuasive constructions of metastable de Sitter spaces within string/M-theory.

Now, I am confident that Cumrun Vafa is one of the staunchest believers in string/M-theory in the world – I might have a hard time to compete with him even when it comes to the strength of the belief. So doesn't he think that this "no-go theorem" for the positive cosmological constant excludes string theory because the positive cosmological constant has been observed?

A good question, indeed. Well, it turns out that Cumrun Vafa has become a quintessence believer. So the cosmological constant isn't really constant, some scalar field is rolling, and its relative constancy only emulates the cosmological constant. As David Gross reminds everybody around 0:58:00 in the video above, quintenessence has a widely believed problem: it seems to predict time-dependent fundamental constants such as the fine-structure constant (the conditions are changing with time).

David Gross came to Okinawa from California.

These predicted variations in time don't have a very good reason to be small. Because experiments exist that prove that the fine-structure constant was the same within an impressive accuracy a few bilion years ago, quintessence seems to be basically excluded.

Cumrun believes that the thing can work in some way but I haven't quite absorbed his new belief – it's still rather non-standard for me.

(Along with Steinhardt and two other authors, Vafa posted an even more recent paper against inflation that tries to suggest that even inflation is in tension with the Swampland rules of quantum gravity. Cumrun has discussed this paper in his talk, too. He would probably replace inflation with the string gas cosmology or something like that – well, it's possible to research it but I think that the string gas cosmology is even less likely to be true than quintessence.)

Around 1:01:00, Eva Silverstein joins David Gross in the criticisms. Both of them have offered some lore that somewhat contradicts Vafa's picture, to put it mildly. Let me say the following: I have gone through similar thoughts, have been exposed to similar arguments, and I also tend to think that the lore is more likely than not.

But something is still wrong with the overall picture of dark energy and other things in string theory so I think it's right to be open-minded. By constantly repeating the lore – and David Gross does it rather often – one may force the quantum Zeno effect on the string researchers. They won't have the opportunity to make a jump that is almost certainly needed.

Cumrun Vafa knows quite something and when he becomes a quitenessence believer, I think it's useful to be interested in the mental processes that have led him to this transformation. Gross repeats some lore but there is really no rock-solid argument against quintessence. In fact, I think that some people could sensibly argue that swampland-like inequalities are actually more solid consequences of a theoretical framework – and you may view them as consequences of either quantum gravity or string/M-theory (which are ultimately equivalent but the phrases "sound" different) – than Gore's lore [I meant Gross' lore but I kept the typo because it looked funny] that disfavors quintessence models.

I have had similar feelings when David Gross was rather heavily attacking (repeated TRF guest blogger) Gordon Kane. You know, I have shared Gross' observation that in his M-theory phenomenology, Kane had to make numerous additional assumptions, some of which were inspired by rather detailed empirical observations (about possible ways to extend the Standard Model to a theory that also agrees with some cosmological criteria).

So while I have never believed that Kane has derived the necessity of his kind of models from the first principles – and indeed, it seems that his prediction of a gluino below \(2\TeV\) has been invalidated – there was something that I disliked about Gross' criticism. It just sounded to me that Gross wanted to discourage the people from thinking about specific scenarios, specific classes of models with some extra assumptions that just happen to look natural.

Well, I would even put it in this way: Gross apparently wanted everybody to treat the whole "landscape" as a set of equal elements and avoid the focusing on any particular elements or subgroups of the vacua because that would be a discrimination. In December, Gross dreamed about the early death of Donald Trump and a month later, he rather brutally attacked mainstream conservative Indians.

But those things are fine, no one cares what David Gross thinks about politics – everyone more or less correctly assumes he's just another cloned leftist in the Academia. However, I feel that a similar constant imposition of his lore and group think is something he does in physics, too. And it isn't right. People like Kane must have the freedom to study and propose realistic M-theory compactifications; and people like Vafa must have the freedom to investigate quintessence within string/M-theory. People must combine and recombine assumptions, pick privileged classes of vacua that look more promising to them given these assumptions and the observations, and so on. If those choices are discrimination, then it is a basic moral duty of a physicist to discriminate at basically all times!

I don't understand his reasoning but I find it (less likely than 50% but) conceivable that Cumrun has some reasons to think that the time variation of the constants might be compatible with their quintessence picture. On the other hand, Vafa admits that they don't solve the cosmological constant problem – why the "apparent" current vacuum energy density is so small.

But the inequality they propose – especially if you assume that it wants to be near-saturated – eliminates the "double fine-tuning" that you would need in generic quintessence models, those that were studied before their Swampland findings. In regular quintessence, \(V\approx 10^{-122}\) and \(|V|\approx 10^{-122}\) are two independent fine-tunings. With the near-saturated Swampland inequality, these two fine-tunings reduce to basically one, they are not independent. So you could say that with the Swampland findings, if established, the quintessence is as natural as the cosmological constant (one fine-tuning by 122 orders of magnitude). Vafa has made additional comparisons of naturalness within the standard or their axiomatic system and theirs seems to win.

Eva Silverstein has joined the polemics with her pet topic that I have been aware of since 2005: the affirmative action for supercritical strings. Supercritical string vacua must be treated on par with the critical string theory's compactifications, there can't be any discrimination. Please: Not again! (You know me as someone who passionately argues about an extremely diverse spectrum of topics. But I think that I have actually never argued as tensely about string theory with a string theorist as I did with Silverstein in 2005.)

The discussion at Strings 2018 made it clear that she has tried to convince Cumrun about that supercritical affirmative action and Cumrun has rejected in a very similar way – and maybe for similar reasons – as I did. Sorry, Eva, but supercritical string theory simply isn't an equally likely or convincing picture of the real world as presented by string theory as the critical string theory is.

The prediction of the critical dimension, e.g. \(D=10\) for the weakly coupled superstring, is one of the first heroic predictions of string theory that obviously go beyond the predictive power of quantum field theories. Some supercritical string world sheet CFTs may be defined but it is much less clear whether these theories may be completed to non-perturbative consistent theories.

In the case of critical superstring theory, S-dualities etc. make it extremely likely that the theory is fully consistent at any finite coupling (because it seems OK at zero and infinity). But in the supercritical case, there are no known S-dualities like that and lots of other arguments in favor of non-perturbative consistency that work in critical string theory simply can't be applied to supercritical string theory.

Moreover, the terms proportional to \((D-10)\) appear in the beta-function for the dilaton, a scalar field that plays a preferred role at weak coupling but that should become a generic scalar field at a stronger coupling. The beta-function for the dilaton dictates the Euler-Lagrange equation of motion that one would derive from varying the dilaton in the effective action.

I actually find it likely that there exists a swampland-style inequality similar to the one that Cumrun just discussed that says that the other terms \(t\) in the equation \((D-10)c + t = 0\) cannot be large enough to actually beat the "wrong dimension term" for \(D\neq 10\). As far as I know, all these questions are rather difficult and convincing justifications for one answer or another just don't exist. In fact, I can imagine that this statement excluding the supercritical string theory's stabilized vacua directly follows exactly from the inequality that Vafa et al. propose: they say that the gradient terms, and \(t\) contains those, are always too small to beat the constant terms \(V\) – and \((D-10)c\) might simply be a constant term that needs to be beaten but is too large.

We don't have a proof in either direction. But that's exactly why Cumrun's open-minded approach "I am not saying you must be wrong, Eva, but what I say might also be right" is exactly the right one.

Eva's claim that all the supercritical vacua, perhaps those in \(D=2018\), are as established and as consistent as the \(D=10\) or \(D=11\) vacua is just plain silly. This claim utterly disagrees with the composition of the string theory literature where most of the "good properties" depend on the critical dimension (and/or on supersymmetry, and supersymmetry is also possible in the critical spacetime dimension only). Silverstein's claim about the "equality" of critical and supercritical vacua is just some unjustified ideology at this point. Maybe the research will change towards the "equality between critical and supercritical vacua" in the future but it's a pure speculation; the critical string theory is much more established today and some future advances may also eliminate the supercritical string theory altogether.

Moreover, such a full legitimization of the supercritical vacua would probably lead to a much more hopeless proliferation of the "landscape of possibilities" than the regular landscape of the critical string/M-theory. The very dimension \(D\) would be unlimited and the complexity and diversity of possible compactifications would dramatically increase with \(D\), too. Maybe mathematics or Nature may make the search for the right vacuum much more difficult than we thought (and it's been hard enough for some two decades). But this is just a possibility, not an established fact. It's totally sensible to do research dependent on the working hypothesis that supercritical string theory is a curiosity in perturbative string theory that may be given one page of a textbook – but otherwise it's worthless, unusable, inconsistent rubbish in the string model building!

Cumrun clearly agrees with this working hypothesis of mine while Eva – without real evidence – is trying to make this assumption politically incorrect. She would love to impose a duty on everyone to spend the same time with supercritical string theory as with critical string theory. That's just a counterproductive pressure that should be ignored by Cumrun and others because the outcomes of such an extra rule would almost certain be tragic.

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