The String Coffee Table

It has been shown in Part I (see also hep-th/0401175) that the modes of the $K$-deformed exterior derivative ${\mathbf d}_{K,\xi}$ on loop space together with their adjoints ${\mathbf d}^+_{K,\xi}$ generate the classical super Virasoro algebra. In the following deformations of ${\mathbf d}_{K,\xi}$ are studied under which the form of the superconformal algebra is preserved. The new algebra representations obtained this way are identified as corresponding to the massless NS and NS-NS background fields. A further 2-form background is found and T-duality is studied for all these algebras.

Motivated by the representation of the classical super Virasoro constraints as generalized Dirac-Kaehler constraints $(\mathbf{d} \pm \mathbf{d}^+)|\psi\rangle = 0$ on loop space, examples of the most general continuous deformations $\mathbf{d} \to e^{-\mathbf{W}}\mathbf{d} e^{\mathbf{W}}$ (with $\mathbf{W}$ an even graded reparametrization invariant operator) are considered, which preserve the superconformal algebra. The deformations which induce the three massless NS-NS backgrounds are exhibited. A further 2-form background is found, which is argued to be related to the R-R 2-form. Hints for a manifest realization of S-duality in terms of a algebra isomorphism are discussed. Furthermore, gauge field backgrounds are considered.

The special representation of the deformations used here allows the construction of covariant Hamiltonians generating string evolution in all these backgrounds. As discussed in [3] this can be used to compute curvature corrections to string spectra.

(Here is a preprint of a paper discussing these issues.)

In the paper

Copeland, Myers, Polchinski, Cosmic F- and D-strings

the authors discuss cosmic strings and F/D-strings on the same footing. I am not sure that I completely understand how the transition from the quantum realm of the F-strings to the classical realm of cosmic strings is performed. Is it sufficient to just mumble “string-string and string-field dualities?”

For instance, when the authors say that experimental observation of cosmic strings might shed light on stringy physics, are they referring to the general “(classical) physics described by Polyakov-type actions” or do they really mean to imply that the observation of cosmic strings would tell us anything about (F-)string scale physics?

Dear Ladies and Gentlemen!

A very interesting discussion has been started at news.groups - it is a name of a USENET newsgroup. If you’ve never heard of “newsgroups”, ask someone how can one use them. Teach your mailing program to deal with newsgroups, and register for news.groups.

Please feel more than free to write anything about string theory - or about the proposal to establish a purely string-theoretical newsgroup - at news.groups right now, because this newsgroup belongs to string theory for a couple of weeks before the internet will vote about the fate of this newsgroup. In fact, you SHOULD join.

You can access this newsgroup via the web, too. See

groups.google.com

For example, a guy interested in string theory pointed out the difference between the narrow and the broad meaning of string theory, and he said a couple of things about Brian Greene’s book and a comparison of a newsgroup on cosmic research with sci.physics.strings.

Come to news.groups to discuss the proposal to found sci.physics.strings - the new and kewl newsgroup that is supposed to have the highest information vs. noise ratio among all newsgroups on the internet.

Your decision whether you will participate or not will influence the opinion of other readers whether string theory is an irrelevant obscure theory studied by a couple of crazy people who are not able to use the internet and who don’t want to discuss anything with anyone, but who eat a lot of money from the state budgets worldwide! :-)

Is string theory important enough today that one of tens of thousands of newsgroups should be dedicated exclusively to string theory?

sci.physics.strings is the proposed name of the new newsgroup and the explanation why it should be created is here.

If someone wants to become a moderator, it is relatively easy to realize this dream at the present!

We will need a huge number of YES votes to make the newsgroup be founded, and therefore you are encouraged to inform all people who are interested in string theory around you.

All the best,
Luboš

Ed Witten’s latest: Is weakly coupled (N=4) Yang-Mills-theory also a perturbative string theory? He conjectures that it is, and that the string theory is a topological string theory deformed by D-instantons.

The topological B-model in question has target space $CP^{3|4}$. The correlation functions of this theory are invariant under transformations that leave the holomorphic three-form invariant. This symmetry group turns out to be PSL(4,4), the symmetry of N=4 Yang-Mills theory!

So could the action just be Yang-Mills theory? Unfortunately not. The topological model (at least the open string sector) produces a anti self-dual field A, and a self dual field G (plus some more stuff). The action turns out to be roughly $L= G dA$, while the true Yang-Mills action would require an action $L= G dA + \epsilon G^2$ where $\epsilon \sim g_{\mathrm{YM}}^2$.

EW proposes that this extra term is produced by the presence of D-instantons in the string theory (every instanton=one power of $\epsilon$). As evidence, he shows that YM amplitudes with n gluons of one helicity and 2 of the opposite helicity can be reproduced in the string theory by including D-instantons (the gauge theory amplitudes are apparently well known for this case).

More generally, suppose this correspondence is true. Then there is a match between the number of D-instantons and the power of $\epsilon$ in the amplitude. The terms with $\epsilon^r$ can be shown to correspond to tree level processes with r gluons of negative helicity, and should be reproduced by processes with (so to speak) r-1 instantons. But an instanton number $r-1$ corresponds to a holomorphic curve with degree $d=r-1$. So this further implies that the amplitude should only be nonzero if the incoming particles all lie on this curve. (Well, not exactly; since the curve could be disconnected. But this gets into messy details.)

So we get the next conjecture: Gauge theory processes with $r$ helicity violating gluons, and at loop $l$, are nonzero only if the incoming particles lie on a curve of degree $d=r-1+l$.

This apparently works for the cases EW considers (amplitudes with 4, 5, 6 gluons). The general proof appears difficult. Even for the specific cases, many details appear to be unclear still.

I should also note that there is an important symmetry S under which the first term in the action above has S=-4, while the second has S=-8. D-instantons need to have a particular value of S in order that they contribute correctly. The required formula is presented in the paper, and a heuristic derivation is given. This is a strong indication that something is working.

On the other side, there are many issues (pointed out already in the paper). All the above only works with the open strings, and the closed string sector is completely mysterious. It is suggested that the closed strings will produce a conformal supergravity theory, and in that case the agreement between the string theory and the gauge theory is only valid at the planar level (i.e. large N). (There are issues with non-planar diagrams as well.)

Anomalies are apparently a major mystery. EW points out potential anomalies in the open string quantization (of what he calls D1-D5 and D1-D1 strings), the holomorphic anomaly of the B-model, the c-anomaly of the N-4 YM theory (how can it be coupled to conformal anything) etc. If even EW is puzzled by these anomalies, I certainly can’t say anything useful here.

Immediate developments seem clear. People will start rapidly calculating stuff in the B-model theory. Particularly to understand the coupling of closed strings in this model. There are several conjectures in section 3 of the paper which might be interesting to prove. There are also suggested extensions to other B-models.

And there is the whole issue of theories with less SUSY. These behave differently at loop level. Lots of stuff to do there potentially.

This environment is very inspiring, I’ll start with a couple of questions right away: :-)

Is there anything known about deformations for SCFTs?

From papers like

Förste, Roggenkamp,
Current-current deformation of conformal field theories, and WZW models

I see that there is some theory about deformations of CFTs based on perturbations of correlation functions.

On the other hand, an apparently unrelatred approach to (infinitesimal) deformations has been studied for a while by I. Giannakis. In his most recent

I. Giannakis,
Strings in nontrivial gravitino and Ramond-Ramond backgrounds

he looks at deformations of the BRST charge of the superstring which leave it nilpotent. He claims that he can incorporate RR backgrounds this way, and indeed, he seems to get the correct (linearized) background equations. This looks kind of mysterious to me, though, because the stress-energy superfield cannot be reobtained from a BRST charge deformed by spin fields, as the author emphasises himself. So what is going on here? Is the BRST charge more fundamental then the superconformal generators?

If Giannakis’ approach is viable, wouldn’t it have relevance for covariant quantization of strings in AdS5 and similar backgrounds? However, I see no citations of that paper.

It seems that this string coffee table works, because you are able to see this sentence. Thanks to Jacques. So what do you Gentlemen think, for example, about the stability of two-dimensional superstrings?

Welcome Aaron Bergman, Robert Helling, Lubos Motl, Arvind Rajaraman and Urs Schreiber, and their brand-new blog, The String Coffee Table.

Should be a lively affair, with lots of interesting discussion on a variety of topics. With this fine list of authors, I worry only about violating some bound on