# Can String Theory really fail to contain a de Sitter vacua?

I was reading a post earlier from Peter Woit's Not Even Wrong blog and came across the following reference to the paper "What if string theory has no de Sitter vacua?" by Ulf H. Danielsson, Thomas Van Riet. The preprint is on the Arxiv here - it isn't clear if it has been published in a refereed journal.

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.

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.

Now I'm well aware that Woit really, really doesn't seem to like String Theory. That being said, the books/papers/videos I've come across over basically my entire life seem to showcase the radical potential for the theory to help us understand the most foundational aspects of our world (replicate standard model, combine quantum mechanics and general relatively, etc.), so this would be pretty shocking to me.

Can anyone explain what might be going on here? Any input is appreciated...

• I guess this can get controversial, so I'll try to be objective and speak from what I can tell. There are several sides in this discussion, even among supporters of string theory as a theory of quantum gravity. The paper Woit is making reference to there, link, discusses how there are several approaches to dS from the point of view of string theory, many that have not been explored in much depth and many that are simply unknown to them, as they themselves recognize, given the extension of the literature. Among the approaches they know, they present a general – secavara Apr 11 '18 at 12:13
• classification as well as their fundamental features and potential issues. This is already a point of discussion, as I think you won't find universal agreement in the community about which are real concerns or not. That being said, hopefully distinct factions see this question and give their opinion and I'd also suggest you to go through the paper as well. – secavara Apr 11 '18 at 12:20
• Oh, regarding your recent edit, it has not been published, but this is standard in the field, that is, to post it on arxiv first and wait for reactions, responses and comments before submitting to a journal. – secavara Apr 11 '18 at 12:34
• @secavara to be fair to Pete it was my edit pointing out that the paper had yet to be published. Given your comments are quite long would it be worth you posting them as an answer? – John Rennie Apr 12 '18 at 4:59

I haven't read the paper by Danielsson and Van Riet, but they seem to be in good company here. Recently, four prominent string theorists wrote a paper that suggested (even metastable) De Sitter space might actually belong to the swampland (be impossible to realize in string theory): https://arxiv.org/abs/1806.08362. In this paper they formulated a mathematical conjecture that places bounds on the possible local minima in field space: $$| \nabla V| \geq c \cdot V,$$ with $V$ the scalar potential (the gradient is taken in field space) and $c$ apparently of order one. This would mean that at positive $V$ (positive vacuum energy), the scalar potential is never at a local minimum. Although the conjecture has not been rigorously proven yet (the authors do provide much evidence for it), it seems that this paper is big news in the string theory community.

The authors suggest quintessence models as a way out; these are models in which the cosmological constant is actually not constant, but a dynamical field. This has other consequences, which I am not very familiar with; one of the possibilities might be that fundamental 'constants', like the charge of the electron, might also change in time.

From a quick scan through the paper it seems there is a hole in the argument. Supersymmetry makes a positive cosmological constant hard to achieve, but supersymmetry is obviously broken at some energy since the universe we see around us isn't supersymmetric. So the fact that string theory is supersymmetry does not necessarily forbid a de Sitter solution.

The authors address this in the paper in the introduction to section 3 where they say:

When SUSY is broken well below the KK scale, one could justify a lower-dimensional effective field description that is a supergravity theory where the dS vacuum breaks supersymmetry spontaneously. This constrains the effective action much stronger compared to models that break SUSY at or above the KK scale. We will not discuss this in any detail further on, so let us mention here that the classical vacua typically break SUSY at the KK scale, whereas the quantum IIB vacua", where SUSY is broken by anti-branes for instance should have SUSY broken below the KK scale.

Phenomelogically we have tended to assume supersymmetry is broken at or around the few TeV scale as this helps explain the low mass of the Higgs boson. Unless I have missed something (which is quite possible since I only skimmed the paper) it appears that the authors don't consider this case.

• Whoever downvoted: I freely admit I may have misread or misunderstood the paper because I read it hastily. If so please post your answer to correct me and if I agree I'll delete this answer. – John Rennie Apr 11 '18 at 17:34