D-branes (a question for experts)

[Demystifier]

I understand that there are boundary conditions that make open strings behave as if they were attached to D-branes. However, what I do not understand, is the following:

What makes such boundary conditions stable?
What forces are responsible for that?
Are D-branes independent physical objects that may exist even without strings?
If yes, are they made of something more fundamental (which clearly cannot be strings themselves), or are they independent fundamental objects just as strings?
Are there generally accepted answers to these questions, or is it something that experts still do not really know?
Is pure string theory without D-branes inconsistent?

Also consider this analogy:
D-branes emerge from strings in a similar way as charges emerge from sourceless Maxwell equations. For example, you can consider a central electric field proportional to 1/r^2, which satifsies the sourceless Maxwell equations everywhere, except at r=0. The singular point r=0 can then be interpreted as a pointlike charge. How much sense such an analogy makes?

 

[R.X.]

OK here an answer, upon request:

I understand that there are boundary conditions that make open strings behave as if they were attached to D-branes. However, what I do not understand, is the following...

D-branes are special cases of extended objects in string theory, ie higher dimensional p-branes which can be viewed as solitons (ie, non-perturbative configurations). D-branes are special in that they can be formulated in a "dual" way where a perturbative description is possible - namely in terms of a world-sheet CFT with boundaries.

Think roughly of a D-brane as a higher dimensional analog of a "pointlike soliton", like a magnetic monopole, in the limit where the "size" goes to zero; in a dual formulation this "monopole" looks like an elementary electron and can be treated in terms of ordinary perturbative QFT.

What makes such boundary conditions stable?

In general, they are not, as D-branes can annihilate with each other, etc. If they are wrapped around a topologically non-trivial, minimal volume cycle of a manifold, they can be stable.

What forces are responsible for that?

Forces induced by exchange of strings, for example.

Are D-branes independent physical objects that may exist even without strings?

Viewed as solitons, yes. For example, a 4 dim magnetic monopole can be viewed as a D-brane (in an appropriate description), and one can then use this description to efficiently compute various quantities. But this monopole "exists" also without any reference to strings and higher dimensions.

If yes, are they made of something more fundamental (which clearly cannot be strings themselves), or are they independent fundamental objects just as strings?

Tricky question ... one often treats them as fundamental objects themselves. But that's not quite accurate. Eg ask is a soliton like a magnetic monopole a fundamental object, besides a gauge boson, or not? Since it is a non-perturbative configuration of gauge fields (plus a scalar field), it can also be viewed as a coherent superposition (or roughly "bound state") of the latter. So from this point of view it is not fundamental. In a similar vein one can view D-branes as coherent superpositions of closed strings ("boundary state").

This question really boils down to a much deeper general question, namely what the meaning of "fundamental" degrees of freedoms is. The point is that there is no clearcut answer for this, because it depends on the regime of the parameter space one looks at.

One of the nicest examples where one can quite explicitly see how things work is the celebrated solution of Seiberg and Witten of N=2 SUSY gauge theory (there is a lot of literature on the web, and it's very instructive to think about). It turns out that in one regime of the parameter space (where the Higgs field is large), the "fundamental" degrees of freedom are the gauge fields; there are also monopoles in the theory, and from the viewpoint of the gauge fields (ie from the viewpoint of a lagrangian description that involves local gauge fields) these monopoles are heavy, strongly coupled, non-local. So one may view them as coherent non-perturbative superpositions of gauge fields.

However, in the regime where the Higgs field is small, the roles of the monopoles and gauge fields exchange: the weakly coupled degrees of freedom are the monopoles, and the the appropriate dual formulation they behave exactly like elementary, local electrons. However, in that formulation, the original non-abelian gauge fields look non-local, solitonic, heavy, strongly coupled, and may be viewed as bound states of the electrons (the monopoles in disguise).

So you see there is no absolute notion of what a fundamental degree of freedom is, and what a solitonic bound state is - it depends on at what regime of the theory you look.

A similar story holds more generally, and in particular for D-branes and strings. So it depends on the regime of what you may call fundamental. For example, in the well-know 10dim typeIIA string, you have strings as predominant local degrees of freedom. However, when you go to strong coupling, then as Witten has shown, the D0 branes act together such as to generate an 11th dimension, and the theory becomes a membrane theory that does not involve strings but membranes as fundamental degrees of freedom.

Are there generally accepted answers to these questions, or is it something that experts still do not really know?

It is as always: some answers are proven, others are generally accepted and believed, and very many things are not known or understood.

Is pure string theory without D-branes inconsistent?

That's an interesting Q. (Supersymmetric) perturbative strings are likely consistent to any given order in perturbation theory, but I guess for non-perturbative consistency, all solitonic sectors and branes must be there. That's hard to proove, though. At least in the celebrated field theory example I gave above, one can show that non-perturbative consistency requires the existence of those monopoles; the original argument was that otherwise the squared gauge coupling 1/g^2 must necessarily become negative, which would render the theory non-unitary. I expect that analogous arguments hold much more generally in string theory.

 

[Demystifier]

D-branes are special cases of extended objects in string theory, ie higher dimensional p-branes which can be viewed as solitons (ie, non-perturbative configurations).

The crucial question is: Configurations of WHAT? Fields? Strings? Something unknown? Or are all these things somehow the same, due to dualities?

BTW, thanks for the detailed explanations!

 

[Sauron]

Well, if someone could give me a single good reason of why an string is stable I would believe the books I read about them and may be became an expert.

Since that for me the most natural evolution for an string is to dispersate into its constituents points.

Of course the same apply to the fundamental M2 and M5 branes of M theory.

 

[Demystifier]

Well, if someone could give me a single good reason of why an string is stable I would believe the books I read about them and may be became an expert.

Since that for me the most natural evolution for an string is to dispersate into its constituents points.

There is a string tension that makes it stable. Just as for a violin string.

By the way, I do not (yet) consider myself a true expert for strings, but let me share with you my happynes that today my second paper on strings has been accepted.

 

[R.X.]

The crucial question is: Configurations of WHAT? Fields? Strings?!

Let's assume were are in a semi-classical regime, where quantum corrections are weak so that one has a smooth geometrical description; ie, a nice low energy effective lagrangian that involves classical gauge and Higgs fields, say. Then solitons correspond to solutions of the classical equations of motion, and are given by non-trivial configurations of those (essentially massless) fields. For example, a magnetic monopole is given by a classical solution involving a gauge and a Higgs field that vary non-trivially in space-time.

So in a nutshell, we talk about classical field configurations made out of the fields that appear in the low-energy effective action.

In string theory this is analogous. However depending on the dimension, there can be additional higher rank tensor fields, and all those fields appear in the effective lagrangian. Again, solutions of the classical equations of motion involving those fields correspond to extended solitons, including now p-branes (a special class of which are D-branes). Since those fields themselves are (typically massless) excitation modes of the string, one may loosely say that the p-branes are coherent superpositions of "massless strings".

A big caveat, however: as I was saying before, only in certain regions of the parameter space (in particular, at weak coupling), one has a nice semi-classical description, and only there it makes sense to talk about configurations of fields that satisfy the classical equations of motion. In other regimes quantum corrections can be strong, and there is in general no definition of a brane in terms of classical field configurations - that's why one needs to adopt the proper mathematical language, like sheaves, to describe "branes" more generally.

Well, if someone could give me a single good reason of why an string is stable I would believe the books I read about them and may be became an expert.

Since that for me the most natural evolution for an string is to dispersate into its constituents points

There is no such thing as constituent points. A string can decay or snap only into other strings, and the lowest energy configuration is going to be stable. See some other recent thread here on a similar issue.

 

[Sauron]

Congratulatons for your paper demistyfier..

About the string tension and the violin analogy..., well, don´t understand it like some kind of irrational attack, I have seen that analogy many times, but I see it an empty analogy.

I mean, a violín string is not stable because of it tension, it is stable becuase there are intermolecualr forces betwen constituent atoms. Tension is just a somewhat fictional force that you introduce simple problems.

But in a fundamental string, well, it can´t be that way, and I don´t see a real alternative. Of course you always can choose the stabilty of the string as a postulalate, but for me it is a ver, very unnatural one.

Investigating about a (very) older theory about extended objects, the knt theory of tompshon, tein, Maxwell (partially) and others inthe XIX century I discovered the had a very reasonable argument (withing the contexto of their knowledge) for considering them. It came for a theorem in fluids mechanics with stated that once formed a vortex in a perfect fluid It would remain stable forever. In their times it was assumed that there was an universal prfect fluid, the ehter. But, of course, once the ehter theory was discarded the theory loosed any support (and Q.M appeared as a much better theory for the microscopial physic). Of course people who believe even nowadays in some kind of ether could claim for an string theory as vortex of that ether (well, maybe), but certainly mainstream string theory physicist hate ether (with good reasons, IMHO).

Maybe if there would be a way to see an string as a solitonic state of somtehing else I could see areason for an (at least partial) stability for them

By the way, in that times the tried to explain spectroscopic results as knotting of two or more vortex. That raised me a new question about string theory. Why strings can´t not knott around themselves?

I mean, if you would accept (as everybody does) that strings are (clasically) stable beeing quantum objects ther would be the possiblity of a closed string could be created in a knotted configuration with another closed string.

And a last question. These is about the polyakov integral and the admited interaction vertex (not confuse with vertex operators). It is allways showed that you can see an split of an string in another two, but, whay about a vertex in which an string splits in thre, four, or in general N strings? What forbides the existence of that vertex?. I admit that perturbative theory with, vertex operators, dhem twists,moduly and teichmuller spaces is something which I have readed a few times but I still don´t fullly understand. But towards my understanding works I don´t see a good reason for multisplitng vertex (or "knotting" vertex if we accept going from Rieman surfaces fto more general complex, algebraic curves with some singular points).

Edit:

There is no such thing as constituent points. A string can decay or snap only into other strings, and the lowest energy configuration is going to be stable. See some other recent thread here on a similar issue.

Why there are not constituent points? Mathematically they are clearlly there (i know T-duality, if I understand correctlly, forbides to see below a certain radious, which ould be the schwasrchild radious, but mathematically there are points). Would we accept it as a postulate? If so once agian it lloks a very unnatural one, at least for me (i sawy your answer afther my post, but I still believe it applies).

In fact for me these is the crucial question because I don´t believe too much in string theory. Things such aditional dimensions seems me reasonable. The vacuums problem or the lack of experimental results, well they are problems, sure, but apparently they are solvable ones. But that of acepting that an string has no points seems to go versus the whole tradition of atomism, and versus the mathemathical notion of point.

About the minimum state of energy argument, it seems a circular reasoning, string can´t decay into a lowes state of energy (probably formed of points) because we don´t admit point particles as possible states. Maybe if it would be created a mixed theory with points and strings, and you could probe that an string can´t decay it would be something I could believe somewhat.

Of course I know it is my personal desbelief. And as such can be easilly discarded, but I gues other people could share similar (maybe not so elaborated) desbelief.

Edit 2. In the same line if somone could create a theroy of point particles which would have string configurations as stable stated it could be a solution. Afther all that previous point particle theory wouln´t have any problem with divrgences of coupling to gravity because gravity would only appear as an "efective" theroy for the strings which would result from that points and would aonly affect the strings as a whole, but not their constituent points. Well, maybe, it an idea I have just had, sure there are serious drawbacks (nor to say that I culd be the only one who needs to see strings from a diferent viewpoint to the usual one)

 

[Demystifier]

Of course you always can choose the stabilty of the string as a postulalate, but for me it is a ver, very unnatural one.

That is fine. You do not have to believe in strings. But the fact is that if one takes this postulate, one obtains a theory that turns out to be a good candidate for a theory of "everything". Pointlike particles, as well as higher dimensional fundamental branes, do not possesses such distinguished properties as 1-dimensional strings do.

By the way, by a reasoning similar to yours, you could also conclude that the 3-dimensional space should also dispersate into its constituent points. But you do not think that way about space, do you? So why could not you think about strings as small 1-dimensional "universes" immersed into the big 3-dimensional (or higher dimensional as quantization of strings actually demands) universe? (Plus time, of course.)

 

[Sauron]

That is fine. You do not have to believe in strings. But the fact is that if one takes this postulate, one obtains a theory that turns out to be a good candidate for a theory of "everything".

Certainly if they wouldn´t have that charasteristic they would be the worst theory ever in physics :p.

Anyway I would like to say that in the times the heterertis string ruled the world people seemed a litle bit worried about these problem. But the "unaofficial" attitude seemed to be that in fact thestringy aspect wouldn´t be taken too seriuosly and that the key point of the therory where the two dimensional conformal fields on the worldsheet which would eventually would guide the theory outside that unfanny stringy status.

But with the D-brane revolution things changed because the string viewpoint gained more and more importance. The fundational stuats of the theory I mention seems to have been forgoten.

By the way, by a reasoning similar to yours, you could also conclude that the 3-dimensional space should also dispersate into its constituent points. But you do not think that way about space, do you?

Well, at least one of us doubt about the stabilty of sapace, Afther all you are questiong the stability of D-Branes. Some string scenaries present the 3-d universe as a D-brane afther all. Also in a compactified string theory viewpoint the 3-D universe could be unstable because of possible tunneling to a diferent vacuum (with possibly some of the dimensions unompactifiying).

In a non stringy context there is not a contradiciton. In flat space-time theories (Newtonian and Mikownsky worlds) the universe is considered to be static (not as string which are dynamics) so there is no reason for dispersion.

In RG the universe is dynamcis. But it´s dynamics is not chaotic (at least in the ordinary secenaries) so points don't evolve into bizarre configurations, such as fractals, which would be, in a certian sense, an inestability for the universe. The only way your argument makes sense is acepting there are aditional dimensions where that points can evolve. Once again that is an string theory (or supergravity theory) problematic. But not too bad because afther all the maximun dimension alllowed universe still is stable against dispersion.

So why could not you think about strings as small 1-dimensional "universes" immersed into the big 3-dimensional (or higher dimensional as quantization of strings actually demands) universe? (Plus time, of course.)

I have considered that posibilitie. So there would be two kind of physic. One outside the string, and on inside. That would mean that the inner string physics is stable against dispersione (just as RG is). Well, would you dar to publish such viewpoint in a peer to peer review? (or maybe arxiv). I don't dare to do the same with the questions I am doing here (at least not in their actual state of development). But that the great thing of forums of course, that you can discuse these things without too much risk ;).

 

[R.X.]

Why there are not constituent points? Mathematically they are clearlly there (i know S-duality, if I understand correctlly, forbides to see below a certain radious, which ould be the schwasrchild radious, but mathematically there are points). Would we accept it as a postulate? If so once agian it lloks a very unnatural one, at least for me (i sawy your answer afther my post, but I still believe it applies).

We had this discussed here before: there are simply no constituent "points" on a string. Namely how could one possibly ever measure or see those? One would need to do a scattering experiment and bounce something off that string. But all what one can do is to take another string and use it "as a probe", ie, scatter it against the given string; what would come out from this experiment would be just other strings, because the only interaction that exists is splitting and joining of strings. This is related, as you say, to the notion of a minimal length scale beyond which one just cannot see. Thus, "points" on a string are not observable and thus, by the Rules of Quantum Mechanics, are meaningless quantities.

One should not literally think about strings as little filaments made of "something else" - they are quantum mechanical oscillators and in order to understand them, one should not use too a naive classical intuition.

 

[Demystifier]

I have considered that posibilitie. So there would be two kind of physic. One outside the string, and on inside. That would mean that the inner string physics is stable against dispersione (just as RG is). Well, would you dar to publish such viewpoint in a peer to peer review? (or maybe arxiv).

But the same is valid for particles as well; there is physics ouside the particle, as well as inside the particle. Of course, in the quantum case this becomes more fuzzy, but there is no substantial difference between particles and strings on that issue. Do I dare to publish such a viewpoint? Yes I do. For particles see e.g.
http://xxx.lanl.gov/abs/quant-ph/0208185
http://xxx.lanl.gov/abs/quant-ph/0302152
http://xxx.lanl.gov/abs/gr-qc/0611037
where I propose that quantum particles never really get created or destructed. Just now I am working on a similar theory for quantum strings. (It seems that this can be achieved for strings in a much more elegant way than for particles.)

 

[CarlB]

Demystifier, I loved your papers on this. I agree that particles are never created nor destroyed, and that this argues against the existence of the quantum vacuum. Another way of putting the same thing is to say that every time a particle is destroyed some other particle (or particles) are created. I gave a talk based on this at the DPF meeting in Hawaii a few months ago:
http://www.brannenworks.com/jpp06.pdf

The discontinuous transformation between wave and particle under measurement is something that has bothered me as well, and while I found Bohmian mechanics a more physical (and less abstract) solution to the problem than the standard BS, I also had difficulty with the Bohmian solution, and felt that the application of an extra time coordinate was needed.

To get the transformation to be continuous, you have to have a way of "collapsing" a wave function into a particle description that is continuous. It is possible to do this with a minor change to the Bohmian theory. I wrote this up back in 2003. See section 5.a, titled "Schroedginer's wave equation as an attractor":
http://brannenworks.com/oldquant.html

It's also clear to me that Einstein's work applies (precisely) to the particle rather than wave representation of an object, but if the wave function and particle descriptions are to be continuously related, one might also expect that the energies of these things should be continuously related. That means that we should expect that we should be able to compute the mass of the particle from the wave function itself.

To do this, one must give up the tradition in QM of normalizing according to probability (and linear superposition does not obey normalization anyway). Instead, one must normalize so that the calculated energy of a stationary particle gives the mass. That is, to unify the particles, we have to suppose that their wave functions induce mass, and we must have that heavier particles should have bigger wave functions.

You have quite a few articles on arXiv, so I have the pleasure of looking forward to reading them all.

 

[Demystifier]

Thanks CarlB! In fact, I joined this forum when I saw your expression of your positive opinion on my work, so, in a sense, you are the reason why I am here.