Friday, November 19, 2004

Tom Banks at Harvard

Note added: this article has been updated, and two talks about two-dimensional string theory are briefly described at the bottom.

As Aaron Bergman and Jacques Distler pointed out, Google started another service:

It is a fulltext search engine through all scientific articles, including all articles from (the PDF files are those that are linked), and it knows about the number of citations. The server lists the article with the given query and it prefers the cited articles.

For example, search for

You will get all the papers that contain these two words, and the papers where the words appear in the title, and the papers with the large number of citations, will be listed first.

OK, let me know switch to the scientific activity at Harvard. My advisor Tom Banks (now at Rutgers, in spring at UC Santa Cruz) is visiting us, and we have a lot of interesting discussions. Tom says, for example,

  • the current research in string theory is not going quite in the right direction
  • the connections with the experiments must be understood better
  • one of the most important particular problems we must understand is the nature of supersymmetry breaking in string theory, and the possible interrelations between supersymmetry and cosmology
  • Tom often emphasizes his viewpoint that the different vacua in string theory really don't belong to the same theory, in the physical sense, because you can't usually create a bubble of one Universe inside another Universe
  • he gave me some useful feedback about the matrix generalization of the CFT techniques
  • he also presented some insights, questions, and criticism about things like the relation between black hole entropy and topological string theory; about the developments in the "landscape"; and many other issues.

Yesterday, Umut Gürsoy from MIT was speaking at the Duality Seminar about his recent work with Hong Liu about the big bang and big crunch in two-dimensional string theory, as understood from the old matrix models. Some points in that talk:
  • Umut talked about the partition sums in "two-dimensional critical string theory", as he called it (the word "critical" seems a bit like a contradiction, but it's just a matter of terminology)
  • their two-dimensional string theory was bosonic string theory on a Euclidean S^1/Z_2 orbifold - the two fixed points of the orbifold are the "big bang" and "big crunch"
  • although he was talking about bosonic string theory, he said that it was non-perturbatively well-defined; many of us thought that this should only be the case of two-dimensional type 0 theories, but Umut explained that he is expanding in the cosmological constant or what exactly was the expansion parameter
  • it seems that he claimed that they can derive the initial and final conditions of the Universe
  • many of us, including Tom Banks and me, thought that they only calculated the transition amplitude between two specific states, and by inserting some operators, they could have calculated the amplitude between any other pair of states

Davide Gaiotto delivered the family lunch meeting, and we've listened to another talk by Ian Swanson (Caltech) at 3 PM which is described in one of the newer articles.

Much like Umut, Davide Gaiotto was also talking about the old matrix models

  • especially the Kontsevich models - or, more precisely, the Seiberg-Kutasov models
  • he's been working on these things with Leonardo Rastelli, and sometimes with other co-authors
  • he presented the derivation of the matrix model as a discretization of a cubic open string field theory
  • one of his main questions were how the Riemann supersurfaces, including the gravitino fields, should be discretized - and he agreed that the superdirections don't carry any local excitations, and might only influence physics by a determinant and some global constraints (finally, it's not really possible to discretize a fermionic dimension more than it is)
Davide also emphasized that the finite N old matrix models are meaningful. My opinion about this issue is similar to Tom Banks': it's just hard for me to imagine that such a matrix model with finite N and a rather generic potential is a part of string/M-theory. Then we would have to say that virtually everything is string theory. In our description, the finite value of N is a regulator, but the real interesting physics only appears for large N.

My general skeptical comment at the end: I don't know where this two-dimensional string theory research is going, and I am not able to recognize progress in these papers. What is exactly better about the papers about this subject that are written today compared to those 10 years ago? We don't live in two dimensions and two-dimensional gravity is diferent from the four-dimensional and higher-dimensional gravity in many respects - it has no local gravitational degrees of freedom, for example. The matrix models don't seem to be constrained too much. Is it really a part of the same string theory as the ten-dimensional type IIA string vacuum, for example?


  1. Hi Luboš -

    I have seen you mention this matrix generalization of CFT a couple of times on sps, and I wonder if you could sketch some of the ascpects that you have in mind. Will there still be a continuous 2-dimensional parameter space with, say, matrix valued fields on it?


  2. The link to Matthew Nobes' blog is incorrect. It is now at

  3. No, Urs, what I am talking about is NOT a conformal field theory, but rather something like that IKKT matrix model. I don't want to give more details at this particular moment.

  4. I guessed that you wouldn't want to say much more about it... :-)

    As you know, I like the IKKT-approach a lot. I'm curious what you'll come up with.

    The old papers on IKKT (by IKKT and others) have sketchy proofs for how closed SFT can be extracted from the Schwinger-Dyson equations of the matrices in the model, so it is plausible that a generalization of CFT is hidden here somewhere (using finite N).

    I am not at all an expert on this, but it seemed to me that this relation between IKKT and SFT was not very well understood with respect to the subtle details related to the N->oo limit and things like that. For instance I haven't seen any worldsheet central charges being extracted from the model.

  5. Hi Urs!

    Thanks for your comments. Some unimportant replies follow.

    There is no "finite N" analysis of IKKT. The physical quantities in IKKT are supposed to be the sums over all values of N. The framework is nonperturbative if g is finite, not N.

    What I am trying to construct is the analogue of the vertex operators (like those in CFT) but in IKKT, and the methods to calculate their correlators.

    I am not attempting to construct any SFT, but just a rule for the S-matrix.


  6. Hi Lubos!

    Some of us would be very happy to hear your "likely updates" :)