The String Coffee Table

Is this just another quantum gravity issue with regards to good observables.

I mean do even *classical* strings on a curved manifold, have spacelike vanishing commutators that don’t depend on gauge choices in general?

I wouldn’t expect them too.

I should have said one loop truncated gravity with say the Nambu Goto action.

But yea I understand the current technical limitations with quantum string field theory.

In QFT, non-gauge-invariant operators need not (and, frequently, do not) commute outside of the lightcone. The commutators of gauge-invariant operators, however, must vanish outside of the lightcone. This is required for micro-locality.

Long before you were born, our forefathers realized that the requirements of unitarity, Lorentz-invariance, and micro-locality could be codified in terms of the analytic properties of the S-matrix.

Veneziano constructed his famous S-matrix as an example satisfying these required analytic properties. Ergo it, and all the string-theoretic constructions which followed from it, satisfy the requirements of micro-locality.

(It is worth noting the recent paper of Adams et al, which I talked about on my blog, which makes very explicit the connection between the analytic properties of the S-matrix and the absence of superluminal signaling.)

Studying commutators of non-gauge-invariant operators (like the string field in string field theory) sheds no light whatsoever on the issue of micro-locality in string theory.

Schroer, presumably, knows this, too. But, then, his paper would be much shorter if he cut out all the obviously wrong stuff.

In my paper I do not say anywhere that string theory has a fatal flaw as a result of localization properties. I only lament a bit that for a newcomer the terminology “string” may be misunderstood to mean that the objects the theory deals with are localized along strings in Minkowski spacetime in the same (quantum) sense as standard quantum fields are localized at a point. To be sure, there are objects (string-localized fields) which only exist in a string-localized form, but they have nothing to do with string theory (they are mentioned with references); that they have infinite helicity towers instead of mass towers seems to be purely coincidental.
I also want to point out that I have nothing against string theory per se, it is the social concommitant phenomenon of string theory which constitutes the backbone of may essay (this is also why I posted it in physics/ it only got to hep-th/ by crossing). I find it conceivable that this sociological phenomenon could have happened with another subject (if famous people especially Nobel prizes give their blessing), infact I allude that it may be manifestation of the Zeitgeist; actually towards the end of my paper I mention such a case (although that one is cooking on a much smaller flame). I am completely in agreement with Fredenhagen, Rehren and Seiler that one only can know what something is supposed to be after one obtained an intrinsic understanding (it does not have to be complete, just a hint). I go beyond these three authors by asking the question that given these shortcomings, what is the reason for its popularity; I seriously think there is something to be understood here. Although I use in my article profound (I think) scientific arguments, I am unable to do this in a scientific style as FRS and since I want to be honest to myself I call it a scientific polemic (in the tradition of Jost) and posted it on physics and society. The FRS paper is really a scientific review whereas my is a scientific polemic (in which I only became personal on one occasion where I did not see any rational way of arguing). The catalyst for writing it at all was of course Susskin’s manifesto and I am astonished that this has not led to any discussion within the string community.
Hoping that this may remove some of the misunderstandings

Bert Schroer

Urs, yes worldsheet gravity. But anyway Jacques more or less answered what I was struggling to ask. Note its already unclear in Minkowski space, nevermind dealing with something else.

I just read Dimocks paper, and its fairly clear I think. In light cone gauge there is no problem with finding good local observables (equation 49) with respect to the *string lightcone* (page 13), but in the covariant case its not clear (even with various additional positive representation constraints).

So I’ll just reiterate what Urs already said in his opening, it seems all of this are artifacts of what gauge you pick rather than some deep intrinsic understanding.

(I sent these comments several hours ago. If they were not lost and still arrive, please remove this copy.)
One more attempt to get some light into the exasperating topic of localization in string theory, although I only raised this issue in connection with the opening mantra of popular string theory talks and with a bit of confusion this terminology creates with newcomers (the chosen terminology is never a matter of life and death concerning the object you want to define, it may however have some bearing on its intrinsic characterization, the big open problem in string theory).
Dimock’s work was done on the bosonic string and he had to cut out the tachyon (i.e. an object with a notorious relation with respect to localization) and hence it would be nice to do it with the supersymmetric string (e.g. start from the nice presentation of Griorge hep-th/0506100 which is very much in the spirit of Dimock’s) to be absolutely on the safe side.
Looking in somewhat more details of Dimock’s result there seems to be a fine point: depending on the internal state of the string the vanishing of the commutator extends into the timelike region up to an invariant “mass” whose position depends on the internal state i.e. the object is “super-localized” in the pointlike sense. This may serve as a reminder that one is dealing with an object with a rich supply of internal degrees of freedom but it is even further away from a string in spacetime. Again I have no problem with this, to the contrary I find it very interesting since it must be a special object of AQFT since it is Einstein-causal and fulfills the spectrum condition (and everything in AQFT which looks like an elephant is really an elephant); the interesting problem would then be to find it in that huge set which comprises local quantum physics. There is of course (as Distler points out, I think) the possibility that the equivalence between the lightfront- and the covariant quantization breaks down, but this in itself would be a very startling issue.
I continue to be surprized that the issue of Susskind’s manifesto (without this I would not have written my article) has not received any commentary in the community.
Bert

Here is a remark I forgot to add.
There is a very simple and concrete illustration of what I (and also Fredenhagen, Rehren and Seiler) mean by “intrinsic”. Consider the Nambu-Goto string (just because of its simplicity). The quantization (e.g. take the lightcone gauge) gives a local field which is really a collection of infinitely many irreducible representations of the Poincare group (the mass tower) where the strength of the different components is governed by the internal state of the string. The question about intrinsicness is: what is the physical principle which selects the tuning of the relative strength of the components i.e. what characterizes this particular “tower” of particles (which you insist should be placed together) from any other more general way of doing this? (The extrinsic answer is of course it happens to come out in the canonical quantization of the N-G string).
Contrast this with the helicity tower of the family of massless infinite helicity Wigner representation. Tis representation is irreducible so the above problem of highly reducible representations does not enter. In this case the string-localization is a consequence of the more basic positive energy Poincare representation requirement (http://xxx.lanl.gov/abs/math-ph/0511042).
In fact this huge family is besides the (m,s) and finite helicity representations (0,h) the third big class of positive energy representation (which Weinberg in his book has dismissed as unphysical without giving any theoretical reason why), it depends on a continuous “Euclidean” mass parameter of the little group. Already Wigner noticed that these objects have very weird thermal properties (see remarks and references in: http://xxx.lanl.gov/abs/math-ph/0402043). They also do not allow a Noether type energy momentum tensor. But who knows, these may be just the carriers of dark matter/energies. It would be very strange if mother nature does not make use out of this third big positive energy representation class (unless one still finds a reason why this third class is “pathological”). Nature seems to follow principles and not recipes and formulas, and quantum nature does not need the helping hand of a classical description; Wigner’s theory may be very limited but it is genuinely “intrinsic”.
Finally I have a question (in particular to Urs Schreiber, since he seems to have experience with conceptual and mathematical questions). Venezianos dual S-matrix model leads to a crossing symmetric one-particle tower (where all the particle poles enter with the correct sign, so that there are no ghosts) description which is well-defined in any spacetime dimension (??). It is the insistence to read the Veneziano construction as a canonically quantized N-G string which filters out the dimensions?? If the answer is yes, then my question would be: why does one do this (see above)?