Last month Cumrun Vafa gave a talk at Stony Brook entitled The Swamp Surrounding the Landscape. Tonight he has a new paper on the arXiv entitled The String Landscape and the Swampland. Vafa appears to be suggesting that, faced with the huge landscape of possible string vacua and the attendant inability of string theory to predict anything about physics, the thing to do is not to abandon string theory, but to head off into the even larger “swampland” of effective field theories that may or may not correspond to string theory vacua. He gives various arguments for why certain effective field theories may not correspond to string theories, but most of these are just something like “the string theory constructions we have looked at so far can’t give this kind of effective field theory”. Since one still doesn’t know what string theory really is, one probably can’t do much better than this. He also assumes that the rank of the cohomology groups of Calabi-Yau threefolds is bounded, which is a conjecture that at least some algebraic geometers don’t believe in.
Throughout his article, Vafa assumes that string theory must be true, asking “how” it will connect to experiment, not “whether” it will. For more than twenty years, string theorists have led particle physics deep into a swamp. It seems peculiar in the extreme that Vafa is now suggesting that, instead of hiking back out of the swamp to dry land, particle theorists should push on deeper into the swampland.
Update: Lubos Motl has a posting about the Vafa paper. It includes the news that Andy Strominger
believes that the program has two basic flaws: the conjectures are trivially correct in every theory of quantum gravity independently of string theory; and moreover they are wrong.
Some of my commenters claim that what Vafa is doing is designed to make string theory falsifiable. I don’t see this, and Vafa doesn’t make this claim himself. This seems to me an example of a common phenomenon. People take a string theory paper that already is going way out on a limb with not very solid arguments, then make a wild extrapolation that goes far beyond what the author claims and use this to promote the importance of the paper in a completely unjustifiable fashion.
To falsify string theory along these lines, one would have to show that it can’t lead to the standard model as an effective low energy theory. Vafa doesn’t claim this is conceivable, and his arguments can’t possibly do this. Most of the examples he gives of effective theories that may not be low energy limits of a string theory are gauge theories of high rank. It’s certainly conceivable that one can argue for something like a bound on the rank of the effective field theory gauge group if it comes from string theory, but there’s absolutely no reason to believe that such an argument can rule out the rank 4 case we care about (SU(3)xSU(2)xU(1)). I suppose one can argue that, if say Vafa can show the rank must be less than 500, and the LHC discovers a new gauge theory sector with rank 501, string theory would be falsified. But that’s kind of like saying that string theory is falsifiable, because if dragons emerge from the LHC interaction regions, string theory would be wrong.
Update: Jacques Distler also has a posting about the Vafa paper. He says he’ll wager that it is “far, far from true” that “‘anything’ is realizable somewhere on the Landscape”, and that “we will learn much” if we investigate this swamp. He doesn’t explain why it’s a good idea for the particle theory community to enter this swamp to investigate it carefully.
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