Musings

Swampy

One of the amusements of this past weekend was listening to Cumrun talk about the Swampland in perpetually-damp Eugene Oregon. I’ve discussed the subject here, before but what surprised me, when I asked him about it in person, was how modest his goals for the program are. He was very focussed on broad, qualitative features of vacua that could (or could not) arise in String Theory. More detailed, quantitative, questions he didn’t think were likely to be addressable in his framework. Perhaps, he was simply being cautious, sticking to things that might reasonably be proven in the near-term. But I think it’s important to state that more ambitious results are conceivable and — if String Theory is to usefully make contact with experiment — even necessary.

For concreteness, let us assume, it turns out that physics at low energies (below a few TeV) is described by the MSSM. This is a theory with no massless moduli, so any String vacua of this type are necessarily isolated. We don’t, currently, know of any String vacuum whose low-energy effective theory is precisely the MSSM (there are examples that come close). But many people confidently assert that the String Theory Landscape ought to contain a large number of such vacua. Let us be charitable and assume that they are correct.

Even so, these points form a set of measure zero in the MSSM parameter space¹. The generic point in the MSSM moduli space is part of the Swampland! Let me say that again: the generic point in the MSSM moduli space does not have a consistent UV completion including gravity; only a set of points of measure zero are UV-consistent.

Moreover, it’s far from clear how those UV-consistent points are distributed within the MSSM parameter space.

• Are they everywhere dense²?
• Or are there “voids” where there are no, or only a few vacua?
• Or do the points lie on, or near, a subspace of positive codimension?

Even if you believe that there are a large number of MSSM String Theory vacua, it’s an entirely separate, and far less plausible assertion that they are dense in the MSSM parameter space. Indeed, the whole point of the “Friendly Landscape” is that (if the Landscape is friendly) they are not dense, indeed, that they are peaked around some low-dimensional subspace of the parameter space³.

Finding genuinely realistic String vacua is a hard task. If we manage to find a large number of them, understanding how they are distributed within the relevant parameter space is yet another challenge. But it may be the one we ultimately need to face, to extract falsifiable predictions from String Theory.