Shamit Kachru (described by Lenny Susskind as the “master Rube Goldberg architect”) and collaborators have a new paper out this evening on flux compactifications, one that in a rational world should finish off the subject completely. Recall that Kachru is one of the K’s responsible for the KKLT construction of these flux compactifications that stabilize all moduli, and for the last couple years debate has raged over whether this sort of construction gives 10100, 10500 or even 101000 possible string theory vacuum states.
Susskind, Arkani-Hamed, and other anthropic principle aficionados have argued that the fact that this number is at least 10100 is a great triumph because it means that there are so many vacua that at least some will have small enough cosmological constant to be consistent with our existence. But if there are too many, all hope of getting predictions out of string theory disappears. With 101000 vacua, you can find not only the cosmological constant you want, but probably any values of anything particle experimentalists have ever measured or ever will measure, and the theory becomes completely unpredictive.
Even so, the study of these vacua has become more and more popular over the last year or two, with many arguing that, no matter how big the number is, at least it’s finite, so you have improved over the standard model, which has continuously tunable parameters. This argument was made in the panel discussion at the Perimeter Institute a month or so ago. Also, a finite number of vacua allows you to study their statistics, by assigning a weight one to each possible vacuum state and getting a probability measure by dividing by the total number. You can then engage in wishful thinking that this probability measure will be peaked about certain values, giving a sort of prediction.
The new paper gives a construction of flux compactifications of type IIA string theory, and in this case the authors find an infinite number of possibilities. This should kill off any hopes of extracting predictions from string theory by counting vacua and doing statistics. The authors try and put a brave face on what has happened, writing:
“we should emphasize that the divergence of the number of SUSY vacua may not be particularly disastrous. A mild cut on the acceptable volume of the extra dimensions will render the number of vacua finite.”
but then they go on to puncture their own argument by noting that:
“one can legitimately worry that the conclusions of any statistical argument will be dominated by the precise choice of the cut-off criterion, since the regulated distribution is dominated by vacua with volumes close to the cut-off.”
With this new result, the infinitesimally small remaining hope of getting predictions out of the string theory landscape framework has now vanished. It will be interesting to see if this slows down at all the ever-increasing number of string theorists working in this field.
Update: Lubos Motl has some comments about this same paper.