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How broad is the term "String theory"?

Typical brief descriptions of string theory focus on the fact that it describes fundamental particles as being string-like rather than point-like, or, more generally, being at least 1-dimensional.

So is any model in which the fundamental particles are at least 1-dimensional a form of string theory? If not, what are the other requirements?

To put it another way, given a specific model, what factors would you consider when deciding whether that model was a string theory model or not?

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Dear @Harry, any relativistic model with extended objects that has at most a finite number of adjustable parameters and avoids short-distance inconsistencies may be called "string theory" and there can't be any other theory matching these constraints besides those that are considered "string theory" by "string theorists". I assure you that if you find another "qualitatively new" solution that matches the simple criteria, and it will be a real working one, not just a crackpot "proposal of a concept", you will become very famous among HEP-TH physicists. String theory is the only game in town. –  Luboš Motl Nov 3 '11 at 10:29
@LubošMotl: can you comment on Ron's answer? In particular, can you suggest a model which you think would be part of string theory but not meet Ron's requirements? –  Harry Johnston Nov 3 '11 at 21:47
@Harry: to be fair to Lubos--- it is very difficult to find an extended object theory which is not standard string theory and which is consistent in the continuum limit. All other examples are horrifically complicated, like self-intesecting strings, but there is no argument against them. The examples I gave all resolve to pointlike particles at short distances, but are stringlike in intermediate energy ranges. Lubos is making a radical claim that extended objects are all that is required, and this claim might be true (epsilon chance). The extra requirements are what were needed historically. –  Ron Maimon Nov 4 '11 at 3:57
@Lubos: While I agree that string theory is the only game in town, I think you are wrong that string theory is the only extended object consistent theory. It is almost certainly the only holographically consistent extended object theory, but there is no way that you can't find scaling polymer limits in a field theory, which are not related to dual strings or to gravity. For sure you can find them in restricted energy ranges, and there is no argument that they do not scale to a consistent limit. The uniqueness arguments in the literature are for dual strings only. –  Ron Maimon Nov 4 '11 at 3:59
@Ron: what puzzles me about what Lubos is saying is that it would seem to make the claim "String theory is the only game in town" almost vacuous. If any GR-consistent theory without point particles is string theory, and since point particles and GR don't get along, then almost certainly any useful TOE will be "string theory" - but this doesn't help us actually find such a TOE, since it doesn't narrow down the choices significantly. –  Harry Johnston Nov 5 '11 at 23:39
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1 Answer

up vote 5 down vote accepted

The "other requirements" are the real requirements, the string business is just a gloss, which omits the most important S-matrix assumptions.. There is another question regarding this here: Are There Strings that aren't Chew-ish? (and the linked discussion explains some of the issues).

String theory is not just a theory of strings. In its simplest formulation, it is a theory of strings which can only interact by exchanging other strings, not by exchanging point particles (or anything else). This excludes things like atomic polymers, or strings made out of points, or strings that interact by self-intersection, except to the extent that you can view the special string-theory strings as made out of string bits, like in Matrix theory.

The historical marginalization of S-matrix theory and its practitioners is the main reason that the string assumption is played up, and the bootstrap assumptions are played down. Bootstrap was politically unpopular, and any theory that said "bootstrap" would be ignored in the 1980s and 1990s.

A good list of requirements on string theory is this:

  • There are strings, so the spectrum of the theory is the oscillation spectrum of a string worldsheet action.
  • the exchange of strings is the source of all the (perturbative) forces in string theory. This means that once you know the string spectrum, you know the interactions are by summing over all intermediate states of the string alone, with nothing else.
  • The scattering is Regge-soft scattering in Regge limits. This requirement is technical, and hard to state for a general audience, so it is left out. What it says is that the sum over all intermediate string states gives cancelling amplitude from particles of different spins, and that these cancellations lead to an amplitude that falls off faster than a power at very high energies. although each spin-n state gives an amplitude that blows up ever harder at high energies. This is sometimes called the bootstrap assumption, the assumption that everything in the theory is a bound state which is part of a family of related bound states which together give softer scattering than each one individually.
  • The exchange of strings in the t-channel is the same as exchange in the s-channel, and does not require counting the particles separately. This gives the world-sheet picture, from the symmetry properties of tree diagrams in such a theory. That the interactions are by worldsheet just is not derivable from the spectrum alone, without the assumption that the spectrum bootstraps, and doesn't resolve to something else at short distances.

These requirements partially overlap, nobody has made orthogonal axioms. Together with the following rule:

  • The string must have a fermionic excitation

They should be enough to uniquely determine the perturbative superstring theories. It is clear that there is at least one string theory that people missed completely, this is Simeon Hellerman's M-theory-on-a-Klein-bottle strings, and there are tons of different vacua which could be thought of as new theories in this formulation, because each S-matrix is a different theory.

These perturbative string theories link up non-perturbatively into an ubertheory called M-theory. A theory today would be called part of string theory if it is a description of some configuration of M-theory. There is no full enumeration of these, so it is impossible to say exactly what a configuration is, although there is a partial list, and there is no real arbitrariness.

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Despite the ignorant downvote, this is a correct answer, and you won't get a better one elsewhere. –  Ron Maimon Nov 3 '11 at 16:51
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