Science News is running a long interview with Murray Gell-Mann, who will be celebrating his 80th birthday tomorrow. Gell-Mann was arguably (Feynman is one who would argue..) the most influential figure in theoretical particle physics throughout the 1950s and 1960s. In the interview, he gives the standard story about the cosmological constant/supersymmetry/hierarchy problem, expecting superpartners to be accessible at the LHC design energy, although perhaps not at its initial energy of 3.5 TeV/beam. If superpartners don’t show up at 7 TeV/beam, he says:
Well, we’d have to see exactly how bad it is. I mean how high up you go and still don’t find anything and so on. But yes, one might have to discard this whole line of reasoning.
Gell-Mann describes himself as not a string theorist, but someone who thought it was promising and continues to do so, claiming:
I was a sort of patron of string theory — as a conservationist I set up a nature reserve for endangered superstring theorists at Caltech, and from 1972 to 1984 a lot of the work in string theory was done there.
He speculates about what is missing in string theory as follows:
I am puzzled by what seems to me the paucity of effort to find the underlying principle of superstring theory-based unified theory. Einstein didn’t just cobble together his general relativistic theory of gravitation. Instead he found the principle, which was general relativity, general invariance under change of coordinate system. Very deep result. And all that was necessary then to write down the equation was to contact Einstein’s classmate Marcel Grossmann, who knew about Riemannian geometry and ask him what was the equation, and he gave Einstein the formula. Once you find the principle, the theory is not that far behind. And that principle is in some sense a symmetry principle always.
Well, why isn’t there more effort on the part of theorists in this field to uncover that principle? Also, back in the days when the superstring theory was thought to be connected with hadrons rather than all the particles and all the forces, back in that day the underlying theory for hadrons was thought to be capable of being formulated as a bootstrap theory, where all the hadrons were made up of one another in a self-consistent bootstrap scheme. And that’s where superstring theory originated, in that bootstrap situation. Well, why not investigate that further? Why not look further into the notion of the bootstrap and see if there is some sort of modern symmetry principle that would underlie the superstring-based theory of all the forces and all the particles. Some modern equivalent of the bootstrap idea, perhaps related to something that they call modular invariance. Whenever I talk with wonderful brilliant people who work on this stuff, I ask what don’t you look more at the bootstrap and why don’t you look more at the underlying principle. . . .
Lubos Motl seems to have calmed down a bit recently, and his latest posting is about the Gell-Mann interview. He describes Gell-Mann as not just a patron of string theory, but a holy patron of string theory, with the comments quoted above “the holy word”. They inspire him as he continues to work a few hours a day towards finding the holy grail of string theory: some fundamental principle that defines the theory non-perturbatively.
Searches for such a principle go back at least 25 years, to 1984 and the explosion of interest in string theory as a unified theory. After the first efforts to base unification on a Calabi-Yau, it soon became clear that more was needed than string perturbation theory. Just one of many such attempts that I remember was that of Friedan/Shenker in 1986, who hoped that in some sense the moduli space of all Riemann surfaces would somehow carry a unique vector bundle with flat connection. There were many others.
Lubos entered the field ten years later, after discoveries about dualities had led to Witten’s conjecture of the existence of an “M-theory” that would reduce in various limits to the known string theories. At the time, the hot candidate for such a theory was something called Matrix theory, and Lubos made his reputation with work on this. His thinking these days grows out of the “M-theory” conjecture that he first started working on as an undergraduate 13 years ago, and probably reflects well the kind of speculative hopes that drove this area of research from the beginning:
It also seems extremely likely that some UV/IR links – modeled by the modular invariance in the context of perturbative closed strings – will be important for the formulation of the ultimate principle. Non-perturbatively, it seems obvious that such a link will have to constrain the black hole microstates, i.e. the generic high-mass particle species in any theory of quantum gravity. The spectrum and detailed structure of the black hole microstates must be linked to low-energy fields and all of their higher-order interactions. These conditions will admit a limited number of solutions that will coincide with the allowed configurations of string/M-theory.
Moreover, it’s conceivable that we won’t be able to work “fully on the worldsheet” or “fully in the spacetime”. I feel that the ultimate set of consistency rules for quantum gravity will work “simultaneously” for the generalized worldvolumes as well as spacetime. So I am spending a lot of time by attempts to import some lessons – and methods to derive or generate new degrees of freedom – from spacetimes to the worldvolumes, and vice versa.
Modular invariance, mutual locality of operators, Dirac quantization rules, similar conditions, and their generalizations play an important role. But it remains to be seen whether there is a concise, ultimate principle or set of principles, why it generalizes the conformal symmetry (and modular invariance) in the perturbative limit, and why it admits old perturbative solutions as well as new, non-perturbative solutions such as the 11-dimensional vacuum of M-theory.
Of course, one of the most obvious testing grounds for such new sets of ideas is the exceptional U-duality group of M-theory on tori – i.e. the maximally supersymmetric supergravity. The exceptional groups are pretty and they must have a pretty cool explanation in terms of a structure we still don’t fully know.
Like Gell-Mann, Lubos expects the right theory to emerge not from choice of a specific set of dynamical degrees of freedom, but by a “bootstrap”: discovery of some sort of consistency conditions that uniquely pick out the right theory. The idea is that you don’t have to get to fundamental variables at the bottom of things to rest your theory on, but can by some other means “pick yourself up by your bootstraps”. Since this doesn’t work in real life, I’ve always wondered why its advocates didn’t pick a more convincing name…
Lubos ends his posting with:
I think that some kind of bootstrap is needed to determine what “M” and its structure of symmetries really is. Is there a third person in the world who cares about this possibly most important question of science? These core topics of string theory are currently understudied at least by two orders of magnitude.
The question of why so few string theorists work on this question is an interesting one. The M-theory conjecture drove string theory research for many years. My own suspicion is that the fact of the matter is that most string theorists have just given up on it. The AdS/CFT correspondence appears to give a non-perturbative definition of string theory in a particular background (in terms of a QFT), and string theorists are more interested in investigating that than in continuing the so-far futile search for “M-theory”. In addition, arguments of landscapeologists indicate that if you did find the conjectured “M-theory”, it might be a useless untestable “theory” that could explain just about anything.
Physicists with a sense of history also have another good reason to be suspicious of calls for a new “bootstrap” program. This idea was all the rage during the sixties, but ended up a dismal failure. The conjecture that some known powerful principles (analyticity, crossing, etc..) would have a unique solution satisfying them just turned out to be wrong as a way of understanding the strong interactions. There are lots of possible solutions, and finding the right theory requires identifying the correct one: an SU(3) gauge theory with a specific, very beautiful set of geometrical degrees of freedom. This theory remains poorly understood, and the project of better understanding it recently has revived some of the bootstrap ideas, but in the context of trying out a new choice of geometrical degrees of freedom (twistors). This is now the hot idea of the subject, but it’s no longer one that promises unification via string theory. I suspect Lubos will be increasingly lonely in the pursuit of the dream of his youth, as his colleagues mostly give up on it and move on.
