The String Coffee Table

The String Coffee Table is a group weblog that is supposed to be a forum for researchers and graduate students in string theory that allows informal but possibly technical discussion of whatever string theory topics they are concerned with, including in particular the discussion of papers that have appeared on the hep-th, gr-qc, hep-ph and related preprint archives.

Everybody can (and is invited to) comment on posts to the Coffee Table by following the links Reply to this or Post a New Comment below each message. The so called hosts of the Coffee Table can furthermore start new discussion threads by writing entries on the Coffee Table’s main page. There are currently five hosts only, but it is planned to invite others as hosts of the Coffee Table in the future.

Participating in and following the discussions at the Coffee Table does not require anything else than an ordinary internet browser, but is most conveniently done using in addition a software tool called an RSS News Aggregator. which handles the RSS (Rich Site Summary) of weblogs. Such RSS readers are freely available, very simple to install and extremely expedient for weblog discussion. They allow to read the weblog in a way similar to newgroups and other online discussion forums. They automatically provide a list of the latest contributions anywhere at the Coffee Table. This way one does not need to search the entire site by hand for unread messages.

There are many RSS readers freely available, for instance SharpReader and NewsWatcherfor MS-Windows, and RSS Reader Panel, Agregg8, NewsMonster as extensions for Mozilla.

After installing the RSS reader it has to be informed about the location of the RSS feed of the String Coffee Table. This is done by entering the URL of the Content Feed and of the Comments Feed. For most RSS readers this can conveniently be done by just dragging and dropping the boxes found under the headline Syndicate in the right column on the main page of the String Coffee Table into the RRS Reader window.

One of the main advantages of the String Coffee Table over other forms of online discussion is its support for properly typeset mathematical formulas using MathML. In order that these formulas are properly displayed in one’s browser it may be necessary to download a (freely available) plugin and/or font. See here for more information.

The inclusion of mathematical symbols and formulas in one’s comment requires choosing the option itex to MathML with parbreaks from the Text Filter menu which sits right above the comment editor pane. Ordinary LaTeX code can then be included inside of $…$ (for inline formulas) or inside of \[…\] (for displayed math). More details can be found in the WebTeX manual.

There are several HTML-tags that can be used inside a comment, the details of which are given right above the comment editor pane.

In particular, hyperlinks are entered as usual by typing

<a href=”url goes here”>link name goes here</a>.

Special characters are entered by typing &cid;, where cid is one of the usual character codes (named entities). A list of named character entities that can be used in the body of a comment is here. A list of named entities that are allowed in MathML is here.
(Also see Jacques Distler’s comment.)

For instance ‘Poincaré & Schrödinger’ is obtained by typing

Poincar&eacute; &amp; Schr&ouml;dinger.

Note that using the blockquote tag, which should be used to quote the material that one is replying to, requires to enclose the quoted text in an extra paragraph. This can be done either by using the paragraph tag or by choosing convert line breaks or itex to MathML with parbreaks from the Text Filter menu and including a blank line below and above the blockquote tags.

More details can be found in the comments.

I wish everybody an enjoyable and fruitful discussion at the String Coffee Table!

The String Coffee Table has been set up and is maintained by Jacques Distler. Many thanks to Jacques for his efforts!

As readers of sci.physics.research might remember, a while ago I had learned about the IIB Matrix Model and had fallen in love with it. Unfortunately at that time I was busy with other things and didn’t find the time to absorb the technical details. Two events now made me have a second look at the literature on this model. One is, maybe surprisingly, my encounter with Pohlmeyer invariants. The other is the review

T. Azuma, Matrix models and the gravitational interaction

which appeared recently.

What do Pohlmeyer inavariants have to do with proposals for nonperturbative string theory? There is at least one intriguing technical similarity:

Pohlmeyer invariants are classical gauge invariant observables of the bosonic string which map any configuration of the string (at constant worldsheet time) to the number obtained by picking any constant $U(N \to \infty)$ gauge connection on target space and evaluating its Wilson line around the loop formed by the string at the given worldsheet time.

In the paper

K. Pohlmeyer & K.-H. Rehren, The invariant charges of the Nambu-Goto Theory: Their Geometric Origin and Their Completeness

it is shown that from the knowledge of the values of all these Wilson lines one can reconstruct the form of the surface swept out by the string.

What does this have to do with the IIB Matrix Model, though?

For completeness let me recall that the IIB Matrix model is obtained either by a complete dimensional reduction of 10d SYM or of a matrix regularization of the Green-Schwarz IIB superstring. Either way one is left with the simple action

Here $A$ and $\Psi$ are $N\times N$ Hermitian matrices and $\Psi$ is furthermore a Majorana-Weyl spinor in ten dimensions. All these objects are constant, i.e. do not depend on any coordinate parameters - there are none in this model.

There are many possible routes to rederive known string theory from this action. Let me just list a few important papers.

The best starting point to read about the IIB Matrix Model is probably

H. Aoki, S. Iso, H. Kawai, Y. Kitazawa, A. Tsuchiya, T. Tada, IIB Matrix Model.

This is based in part on

M. Fukuma, H. Kawai, Y. Kitazawa, A. Tsuchiya, String Field Theoy from IIB Matrix Model,

where intriguing hints are given, that Wilson loops in this model of constant gauge connections satisfy the equations of motion of closed string field theory. I’ll have to say more about this below. Here I just note that this way of reobtaining strings from the IIB model is complementary to realizing that the action $S$ above is the matrix regularization of the $GS$ action. In fact the authors argue that one way one arrives at F-strings, while the other way one arrives at D-strings.

This is incidentally the point where the idea behind the Pohlmeyer invariants reappears in the IIB Matrix Model: In both cases Wilson loops of large-$N$ constant connections around a loop describe physical configurations of a string which is identified with this loop! Of course this is nothing but an aspect of string/gauge duality, somehow, but it is a particularly nice one, I think.

In order to see how the IIB model fits into the very big picture the paper

A. Connes, M. Douglas, A. Schwarz, Noncommutative Geometry and Matrix Theory: Compactification on Tori

is probably indispensable. Therein it is discussed how the compactified IIB Matrix Model is the same as the BFSS Matrix Model at finite temperature!

T. Azumo has more interesting references in his thesis paper. One of them looks like a valuable review text, apparently private notes by S. Shinohara, but unfortunately (for me!) this postscript is written in Japanese! :-)

I want to say more about the IIB Model soon. Today my aim is to get started by trying to work out the central steps involved in the proof that Wilson loops of the IIB Matrix Model satisfy equations of motion of string field theory. I am motivated by the fact that the respective derivation in the above mentioned papers involves some rather messy looking formulas which unfortunately may obscure the absolutely beautiful mechanisms that are involved. These are what I want to work out.

I was asked by A. Pelster, who has worked on torsion gravity together with H. Kleinert and F. Hehl, if I consider it worthwhile thinking about torsion gravity in the context of string theory.

Of course everybody knows that there is the Kalb-Ramond field in string theory whose field strength acts like a torsion in many situations. For instance in the highly important (S)WZW models the Kalb-Ramond field provides the parallelizing torsion of the group manifold that the string is propagating on.

Apart from that, the Kalb-Ramond field of string theory is perhaps more prominently known for its relation to noncommutative field theory, as described in the seminal paper

N. Seiberg and E. Witten, String Theory and Noncommutative Geometry .

Now A. Pelster points me to papers by Richard Hammond, who has done very detailed studies of torsion gravity in general as well as its relation to string theory in particular. The most comprehensive review article is apparently

R. Hammond, Tosion gravity.

When challenged, I realized that I couldn’t satisfactorily answer why I had heard so little about the role of the Kalb-Ramond field as providing spacetime torsion. Together with R. Hammond, A. Pelster likes to argue that, since the Kalb-Ramond field is not at order $\alpha^\prime$ in the string action but on par with the gravitational terms, it should actually have measurable effects even at relatively modest enegies - shouldn’t it?

Indeed, R. Hammond, who discusses experimental signatures of torion in great detail, argues that any detection of torsion would have direct implications for the experimental verification of string theory. In his above paper he conculdes

We have seen that torsion is called on stage by many directors, from string theory to supergravity, yet the audience has not yet settled on the correct interpretation of its role. I believen any diract, or even indirect, observation of torsion would be one of the greatest breakthroughs in many decades, and would certainly help settle these questions.

I should try to better understand the big picture of torsion gravity in string theory.