## Thursday, September 29, 2005 ... /////

### Swampland

Some people may think that the stringy landscape is huge which may imply that anything goes. But Cumrun Vafa explains that even if the landscape is as large as the maximally anthropically religious people in the field say, it is not the biggest thing in the world:

The landscape is surrounded by a much bigger swampland which includes effective field theories that seem consistent as effective field theories, but become inconsistent for subtle reasons if you want to couple them to quantum gravity i.e. realize them within string theory.

Such a claim means that Cumrun - together with several of us who are thinking in the same way - has a couple of general background-independent statements or predictions about string theory such as the finiteness of its moduli spaces - which includes finiteness of moduli spaces of conformal field theories (measured by the Zamolodchikov metric; note that everything in this statement about CFTs is well-defined); both upper and lower bounds on the number of low-energy fields, and other things.

The new paradigm is once again that the stringy landscape is still a small and special part of a much larger swampland. And even this swampland is embedded in a much more gigantic s**tland of inconsistent field theories and theories of quantum gravity, but Cumrun chose not to discuss this very broad context of his observations. ;-)

(This is really off-topic but if you're interested in the most general jargon, s**tland is a small part of f**kland of ideas about physics that are not even wrong. In the real world, Scotland is not a part of the Falkland Islands, but in physics, it's different.)

I think Cumrun's is a very appealing proposal - one that could be important for our understanding what string theory is and especially what string theory is not. All of us could try to derive some inconsistencies - for example, worldvolume anomalies and contradictions with holography - in various theories that may be legitimate as field theories, but become impossible as backgrounds of string theory.

Can someone present a convincing proof that a background of string theory - even beyond the vacua known today - cannot have U(1)^{496} gauge group in 10 dimensions? Or can you find a stringy realization of this N=1 SUGRA/SUPER-YANG-MILLS? Can you find infinite-volume moduli spaces in string theory or CFTs with infinite volumes? Do they have a discrete spectrum?

There are many questions. And some sceptics may think that all no-go theorems will be wrong because some no-go "theorems" have been shown incorrect. But there are reasons why Cumrun or me believe that this is not the case, and some general statements about the stringy vacua will survive an arbitrary number of superstring revolutions. No doubt, the survivors will be the fittest: which ones they are?

Criticism

I should mention that not everyone is excited with this new program. For example, A. 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.

Although A. may be correct, I would respond to the first objection that it is not a goal to distinguish string theory from a generic consistent background of quantum gravity; on the contrary, it is a part of the belief system in this context that the class of string-theoretical backgrounds and consistent theories of quantum gravities are probably identical sets. The response to the other objection is that while we can't prove most of the conjectures because a complete definition of string theory is lacking, some of them may be true and common features of all string backgrounds may be a good guide in the search for the ultimate formulation of string theory.