### String Localization, Once Again

#### Posted by Urs Schreiber

In

Bert Schroer
*String theory and the crisis in particle physics*

physics/0603112

the main technical argument, apart from several sociological arguments ($\to $), is a certain subtlety in the commutators of string fields.

Bert Schroer interprets the nature of these commutators as saying that from the intrinsic point of view of quantum string field theory strings are *pointlike*, and this he regards as a fatal flaw, as far as I understand.

We had discussed this at great length a while ago with Bert Schroer himself here on the Coffee Table ($\to $).

The relevant literature ($\to $) is

E. Martinec
*Strings and Causality*

hep-th/9311129

as well as

H. Hata, H. Oda
*Causality in Covariant String Field Theory*

hep-th/9608128

and in particular

J. Dimock
*Local String Field Theory*

math-ph/0308007 .

At least superficially, there appears to be a certain disagreement between these results. According to the last paper, two free, bosonic string fields have vanishing commutator if the *center of mass* of the two strings described by the two fields are spacelike seperated.

The first two papers, however, seem to come to the conclusion that the excitations of the string (its spatial extension) also enters the string field commutator. In our last discussion, this was confirmed by Barton Zwiebach ($\to $).

I must admit that I have not taken the time to look at this closely enough to sort this out properly. I had asked J. Dimock about this ($\to $), who replied that there is no contradiction.

One obvious but easily overlooked fact at least seems to be important to note:

What is usually called the *center of mass* of the string is not in any way an intrinsic, invariant quantity.

What is usually called the “center of mass” is really the “center of coordinate density”, if you like. It depends on the parameterization of the string and hence on whether or not any gauges have been fixed.

Of course, when the string is quantized in the usual way, there is a natural and obvious choice of “center of mass mode” which does play the role that one would expect naively. But in particular if one is interested in “intrinsic” properties of quantum systems, one should probably be careful with interpreting any condition that involves the center of mass of two strings too literally.

In any case, even if we agree that two free string fields commute precisely when their respective “centers-of-mass” are spacelike seperated, I don’t quite see why this is supposed to be problematic.

I think the question is this: are we facing technical inconsistencies or just inconsistencies with our intuitive expectations of what technical results should look like?

Posted at March 29, 2006 7:48 AM UTC
## Re: String Localization, Once Again

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.