Way back in 2005, soon after the emergence of the “String Landscape” and the ensuing debate over whether this made string theory untestable pseudo-science, Cumrun Vafa in response started writing about the “Swampland”. In contrast to the “Landscape” of effective field theories that are low energy limits of string theory, the “Swampland” is the space of effective field theories that are not low energy limits of string theory. One motivation here is to be able to claim that string theory is predictive, since if you can show a theory is in the Swampland, then string theory predicts that theory doesn’t describe our world.

I wrote a couple blog postings about this back then, see here and here. The situation was rather comical, with Jacques Distler unintentionally making clear one problem with the whole idea. He was enthusiastic about it, and gave as one example the suggestion that one and two generation versions of the Standard Model were effective theories that could not be derived from string theory, but Volcker Braun immediately wrote in to tell him about such a derivation. At this time I started having my problems with the arXiv (and its moderator, Distler) about trackbacks, but that’s another story.

I haven’t paid much attention to the Swampland business since then, but noticed last night a new preprint with the title What if string theory has no de Sitter vacua?. The authors summarize their argument:

From this analysis we conclude that string theory has not made much progress on the problem of the cosmological constant during the last 15 years. There is a general agreement that the presence of dark energy should be an important clue to new physics. So far, string theory has not been up to the challenge. Or to be more precise, string theorists have not been up to the challenge. The well-motivated introduction of the anthropic principle and the multiverse, was a big relief. The mathematical standards were lowered, and unconstrained model building could set in exploring a wild and free landscape of infinite possibilities. But beyond this suggestive connection between a possible multiverse and the rich mathematical structures of string theory not much solid results have been achieved. We reviewed some fraction of the mounting evidence that most, if not all of this landscape, is a swampland and we refer to [14,16,149] for similar lines of thought. We believe it makes more sense to listen to what string theory is trying to tell us, then to try to get out of the theory what one would like to have. In recent years, especially with the program of the Swampland [14, 150–152], there is luckily a growing community that embraces this idea. Perhaps this program really already made its first prediction: no measurable tensor modes in the CMB. From what we have seen so far, we believe that the most sensible attitude is to accept there are no dS vacua at all because string theory conspires against dS vacua.

The suggestion here is basically that effective field theories on a deSitter background are in the Swampland, so can’t be derived from string theory. Since we seem to live in a deSitter space, the obvious conclusion to draw from this is that string theory is falsified: it can’t be the fundamental theory we are looking for. The authors discuss various unconvincing ways to try and avoid this conclusion.

By the way, the authors make the usual flawed argument that “the string theory landscape is just like the Standard Model”:

This kind of criticism is, however, misguided [10, 11]. One might compare with quantum field theory, where there is an infinity of fully consistent theories. Experiments are needed to pick the right one, and parameters must be fitted. When this is done the theory still has enormous predictive power, and no one would claim that the Standard Model is useless. One could argue in a similar way concerning the string landscape.

They also claim:

Paradoxically the critics of string theory and the proponents of the string landscape all agree on one thing: the landscape exists and we more or less know its properties.

At least this string theory critic has never agreed on this. I don’t believe “string theory” is a well-defined enough framework to answer the question of what all its ground states might be, or to properly characterize them. If you accept conjectures about the theory put forward by the landscapeologists, all evidence is now that the set of ground states they identify is so large as to make predictions impossible. The argument against string theory is that there are two possibilities here: either the theory is too poorly understood to tell us what its ground states are, or it does tell us something, and there are too many ground states to make useful predictions. Either possibility leads to the same conclusion that this is a failed idea.

It is rarely acknowledged just how serious the problem of a lack of a definition of “string theory” really is. To get some idea of how bad this problem is, one can consult one of the main references in this paper, a survey of the Landscape and the Swampland, based on Vafa’s 2017 TASI lectures (this paper also discusses the idea that deSitter is not in the Swampland). Claims are often made that AdS/CFT resolves the problem of defining a non-perturbative string theory of quantum gravity, but in the paper one finds:

We can now ask the question if using this AdS/CFT correspondence gives a non-perturbative definition of string theory. The motivation for this is that we can give a non-perturbative definition of SYM theory, for example by lattice regularization, whereas the holographic quantum gravity dual theory in AdS has no complete definition. The fact that the CFT side, i.e. the non-perturbative definition of SYM, gives in principle, a non-perturbative definition of the AdS side, is of course true. But this may be not very useful for deeper questions of quantum gravity. In fact the regime that the gravity side is weakly coupled is big corresponds to when the SYM is strongly coupled. In fact ‘t Hooft was trying to use string theory as a solution to the gauge theory question at strong coupling and not the other way around!… we find ourself back at the beginning: we want to know fundamentally, what is quantum gravity? It should describe the quantum fluctuations of the metric. From a brief analysis of the standard Einstein-Hilbert action, we see that fluctuations of the metric at the Planck scale should become very violent, leading to potential changes in the topology of the spacetime [103, 104]. This leads naturally to the idea that quantum gravity should be equivalent to summing over all spacetime topologies and geometries:

$$Z_{QG} \sim \sum_{\text{top. and geo.}} e^{-S}$$

In general we have no idea about what description will lead to the correct sum over geometries and topologies. We only do know that there should be some mechanism that washes out the Planck scale fluctuations to produce a smooth space at lower energies. It seems that this description must come from some new fundamental principle, rather than from some duality such as mirror symmetry or AdS/CFT. This lack of knowledge of describing the gravity side quantum mechanically is “the missing corner” in our understanding of string theory.

In both this survey and the new paper, the tactic of trying to remove the Landscape to restore the predictivity of string theory hits up against the obvious problem: you’re left with no theory at all (the equation above, with an undefined sum and an undefined action, is the essence of no theory).