Wednesday, October 27, 2004

Strings in the old days

Last year, I attended the Johns-Hopkins workshop that was held in Gothenborg, Sweden. That was a nice small conference, that included a pre-meeting the week before the actual workshop in which some early participants just gathered at Chalmers University and chatted about all kinds of subjects in string theory (integrability of N=4 SYM was hot that summer and Dijkgraaf-Vafa was quite recent as well). Mans Henningson invited the whole crowd for dinner at his house which was especially nice! Thanks Mans!

As a souvenir from that workshop I brought with me a book with proceedings. That is not so unusual, but in this case these were the proceedings of the Nobel symposium on Particle Physics in 1986. The conference name however is not telling the truth, it was more about strings than about particles. It is really amusing and amazing to read in this volume. Obviously, this was before the second string revolution of the 90s but there are some hint already around.

It starts out with a picture of all participants (18 years from today). Once I found a scanner I will let you participate in this picture, so far I can tell you that I am able to recognize the following people (in no particular order): Green, Van Nieuvenhuizen, Schwarz, Gross, Witten, 't Hooft, Ellis, Hawking, Salam, de Wit, and Fiedan. The list of participants is much longer but the picture is not of supreme quality.

The first contribution is a review by Michael Green that starts out with an expose of Regge behaviour of scattering amplitudes (much more detailed than chapter one of GSW) and then covers all the 'recent' developments. Michael finishes by listing 245 references which costed him quite some efford as he told me. Then comes Olive about KM algebras and Alvarez-Gaume about anomalies and index theorems, Gross explains the heterotic string (mainly text, very few formulas). Many more contributions follow, Witten talks about string field theory as do many others.

In the end, it gets particulary interesting, when they predict what will happen next. John Schwarz' contribution has the title 'The Furture of String Theory'. So let's see, what he predicts: He lists six approaches to string theory: 1) operator methods a la Olive, 2) Polyakov's path integral, 3) 2d CFT by Friedan and friends, 4) 10d effective action 5) light cone gauge field theory 6) string field theory and he predicts "All six approaches wil play an important role in the future developments". OK, he got that mainly right.

Then he talks about background independence, but I guess that will have to waiut for the next twenty years. His next prediction is that type II and heterotic will be shown to be finite at all orders of perturbation theory. Thank's to Berkovits, he got this right as well. His next prediction is "World sheets of infinite genus will plau an important role in future nonperturbative string theories.": That was only half fulfilled: Nonperturbative methods were at the heart of the recent developments, that's right, but I don't know anybody who thinks about those in terms of infinite genus worldsheets.

The next point is the uniqueness of the theory. He quotes Harvey who said that "various heterotic string theories are really different versions of the same theory" and then predicts "It would be most satisfying if there were only one string theory, which is the correct microscopic theory of nature...Presumably the heterotic theory shoud be the survivor. If this is going to happen the type I and type II superstrings would have to be found to be either inconsistent or equivalent to the heterotic theory". Well, M(other) decided for option 2.

The next prediction is an easy shot: "Future progress in string theory will be accompanied by significant advances in mathematics". And the last one is probably the best one: "String theory will be an even more vital and active subject at the turn of the century than it is today [1986]".

The conference summary is done by Gell-Mann. Among many other things that I do not have time to report on right now, he mentions Luis Alvarez-Gaume as giving the lecture that should get the sublimal award for the meeting for flashing transparencies at the highest rate. He reproduces a page from his notes (I should scan that as well), that reads

picture of worldsheet ----> some flat diagram, phi=integral dphi not single valued...IMPORTANT....???...1) phi --> phi+const. 2)------ [two more transparencies]...??...Assume winding of soliton around a-cycles and b-cycles ==> 3rd term... 2nd term computated in holonomy... 1st term??? ...S=S1+S2+S3

And he mentions S-duality of type I and Het-SO(32): "Ther is even the half-joking suggestion of Ed Witten that the two SO(32) theories might be physically equivalent, is such a way that the dilaton field phi is one formulation is related to phi^(-1) [should be -phi] in the other." You can find this conference on spires

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