Lubos Motl has an interesting post on sci.physics.stringsthat gives a detailed explanation of the current state of string field theory.
One way of motivating quantum field theory is to start with a “first-quantized” quantum theory of particles (perhaps defined by integrating over paths), then “second-quantize” by considering a quantum theory of fields, where the fields are defined on the space the points in the path move in. The natural generalization to string theory would be to start with the “first-quantized” theory of strings given by doing path integrals over the possible worldsheets traced out by the moving strings (these are conformal field theories), then “second quantize” by quantizing fields defined on the infinite dimensional space of loops. It has always been a hope of string theorists that this would somehow give a true non-perturbative definition of string theory.
Lubos explains what some of the problems with this idea are. For one thing it is in conflict with the M-theory philosophy that a non-perturbative theory should involve on the same footing not just strings, but also higher dimensional “branes”. He goes on to speculate about what can be done about this problem, saying that perhaps one shouldn’t be trying to find a fundamental set of degrees of freedom and an action functional of them. Instead maybe one just needs to find a set of self-consistent rules, which will be obeyed by all sorts of different degrees of freedom. As he notes at the end, this is similar to the old “Bootstrap Philosophy” of Chew and others that dominated thinking about the strong interactions during the 1960’s. It didn’t work then, and I’ll bet it won’t work now.
June 14, of course. The spelling “Deseret” is due to APS News, though.
Peter, here is a second-hand quote from the Aug/Sept issue of APS News:
“I hope they’re wrong, but I can’t prove it. And I bet my life work on their being wrong.”
-Andrew Strominger, Harvard University, on skeptics who say that there’s nothing to string theory, Deseret Morning News (Salt Lake City), June 41, 2004.
It seems to me that your voice is being heard. But AS is perhaps referring to Glashow and Veltman.
Yawn.
Most of what Lubos says I agree with.
However, I think that the string community has been a little over critical of string field theory. Many theorists would even like to forget its existence, frequently saying that string theory has “no nonperturbative definition.”
As far as we know, Witten’s cubic open bosonic string field theory gives a full nonperturbative definition of open+closed bosonic string theory. This is not to say that every concievable nonperturbative result in string theory has been reproduced in string field theory. It just means that we have no definitive argument that such nonperturbative information is not there, in principle.
String field theory is a very complicated formalism and is far from unique. There are an infinite number of string field theories, each corresponding to a choice of conformal background and a particular decomposition of the moduli space of Riemann surfaces. There are open string field theories, closed string field theories, open+closed string field theories, superstring field theories… Presumably, each of these could provide a nonperturbative definition of string theory, but certain features which might be obvious in one string field theory (such as the perturbative spectrum around its conformal background) may be quite nontrivial in another (one would first have to construct a classical solution describing the background, and then study fluctuations about this solution). All of these formulations are presumably related by a complicated field redefinition, but our current understanding is primative.
Faced with this situation, most string theorists hope that a more elegant, background independent formulation of string theory will at some point present itself. Personally, I have been inclined to take string field theory seriously, hoping that graudually a deeper understanding of its complicated but presumably profound struncture will emmerge.
Brian Greene is doing next week’s physics colloquia on this topic. I’m curious to go, but not curious enough to miss a class that takes attendance 😉
How many places has Chew’s “bootstrap philosophy” worked to even a small degree? The only cases I can think of offhand would be some semi-contrived two dimensional models which appear to be exactly solvable. (ie. quantum inverse scattering sort of stuff). Other than that, I would be hard pressed to think of anything else which was not a failure.