What are strings made of?

Question

This is a potentially naive question that no book adresses and I am not sure if it even makes sense. The question is what are strings (superstrings) made of? I mean, they are named as "objects" which extend in 1 spatial dimension and 1 temporal.  I mean, should they not be made out of some "stringy material" even at very short scales? They are closed or open. In QFT a particle (like the electrons and the quarks) is a the localized excitation of a quantum field. But I fail to understand the concept of "object" in string theory. 

Comments

It seems there's a related old question on Physics.SE, with some good answers too.

Answer 1

What's an electron made of? What's a neutrino made of? If they are really fundamental particles, then the whole point is that they are not made of anything more fundamental. If however string theory is a theory of nature, then electrons are made of string. Now we are back to step 1. If the string is fundamental, then it's not made of anything else, that's the whole point of being fundamental. Of course if M-theory is right, then the string is made of membrane. And we are back to step 1. What's the fundamental membrane made of? If it's fundamental, then it's not made of anything else. On the other hand, if AdS4/CFT3 is right, then the membrane is sort of made of string. At which point you may feel confused.

More seriously, it is important to realize that when we get to fundamental physics, then everday concepts of existence are far behind us and all there remains is some mathematics and a way to deduce scattering cross sections from it. Perturbative string theory is a piece of mathematics that spits of scattering cross sections. It does so by computing correlators of some given 2d superconformal field theory and integrating them over the moduli spaces of super Riemann surfaces, for all genera. That's one big formula, called the string perturbation series, but whatever it actually does, in the end it spits out elements of an S-matrix. And there is a rule for what it means to compare these to scattering experiments. Given that, before you even ask "what is the string made of" you should ask "where do you see a string in the first place"? Ultimately, speaking of "1-dimensional objects propagating through spacetime" is a story that helps think about what that big perturbation series formula actually does. Of course it's a very good story, and so it's used all the time, and as with all stories, after a while one gets a feel for it and it seems obvious and real.

But asking "what's the string made of" is much like asking for the reality of virtual particles. Ultimately there is just a formula, now called the Feynman perturbation series, and it does something and spits out elements of an S-matrix which are being compared to experiment. Virtual particles are just a story that is told which helps think about what this big formula does. And it's a very good story, and so it's used all the time, and as with all stories, after a while one gets a feel for it and it seems obvious and real. But no matter how real it seems, the virtual particles in QFT perturbation theory are a figment of our imagination that helps navigate the realm of fundamental physics which is far, far away from what our minds evolved to being able to visualize. In the end there is just some mathematics which spits out observable numbers. And then people tell a story around it.

Comments

@UrsScreiber Much as this is a good answer, +1, it seems to say that strings (branes) are indivisible components of string (brane) theoretical models, but of itself this doesn't seem to preclude models in which strings or branes are compound objects or emergent from a different kind of model.

Is your philosophy of mathematics as anti-realist as your "the virtual particles in QFT perturbation theory are a figment of our imagination" suggests? I try to write to be readable as either realist or anti-realist about mathematical and physical models.

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@Urs Schreiber This is a really good answer indeed.

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@PeterMorgan, my point is that speaking about reality at the Planck scale in English instead of in Mathematics is not being objective realist -- but is being naive. May Galilei be my witness. Since you bring up philosophy, I might go further and claim that the disrespect theoretical physicists express against philosophy only highlights their own shortcoming: the lack of a development of mathematical metaphysics. I believe it's possible, but, in case there is interest, we should move any further discussion in that direction to PhilosophyStackExchange.

Answer 2

To offer my point of view, after the excellent answer of @Urs Schreiber, my answer to what strings are made of is... strings and more strings and strings and so on. Think about it, strings are conformal in the sense that if you chop a string you get more string. The best way to think about it is indeed as a 2d SCFT. You start with a Green-Schwartz action and solve the theory (if you can). Some details are given in the previous answer. Especially when the string length approaches the Planck length spacetime does not even make sense. When talking about something so fundamental (in some sense) it is absolutely pointless to try to interpret and try to understand what a stringy material would be (as it would be a stringy rubber for example). Also, how much sense does it make to ask "what is a 1 spatial dimensional object made of"? For all I know, I consider strings in the sense Urs mentions. The question it self is indeed ill-defined.

Answer 3

Lenny Susskind explains that the answer to this question depends on the parameters of the theory starting at 1:10:50 until the end of this video.

He makes use of the fact that the question if strings are fundamental or if they are composed of something else is analogous to the question if in electrodynamics, electrons or magnetic monopols have to be considered fundamental to be able to develop a perturbation theory with Feynman diagrams.
It can be shown that magnetic charges $q$ and electric charges $e$ are related by

$$ e\, q = 2 \pi$$

This means, that if the charge of the electron (and therefore their mass) is small, the charge of the magnetic monopoles (and their mass) is huge and vice versa. If the charge and the mass of the electron are small, the electron is considered fundamental and a converging theory (QED) can be developed because the coupling constant $e$ is small. At the same time the magnetic monopoles are heavy complicated things composed of whole bunches of photons and magnetic charges because the coupling constant $q$ is large. This regime corresponds to what we observe with QED being a weakly coupled theory and the magnetic monopoles (if they exist) being to large to be observed. Increasing the electric charge of the electron would lead to a transition to a regime, where the electons become heavy and complicated and in this case it would be more useful to consider a quantized electromagnetic theory with the ligth magnetic monopoles described as fundamental particles.

A similar relationship as described to hold for the pair of electric and magnetic charges exists in string theory between fundamental (f-) strings and D-branes. Depending on the parameters of the theory, either it is more appropriate to consider the D-branes as complicated heavy things composed of fundamental strings, or the D-branes are light and fundamental whereas strings are heavy and complicated things composed of D-branes. The technical term describing this ambiguity is S-duality.

In summary, a unique and universally valid answer to the question what strings are made of can not be given; it depends on the parameters of the theory and the context if it is more useful to consider strings or D-branes as fundamental.

Comments

I am not sure if this is a bit too hand-waving or popular (?) ...

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@Dilaton thanks for your answer which is a good one but more related to what we consider fundamental degrees of freedom and what not. It is about the E/M like duality, I get it. My question, I think, is simpler and less well defined. What are the strings, and correspondingly the D-branes made of since the are extended in some spatial dimension(s). This is why i gave the QFT analogy.

Answer 4

Maybe you might be interested what Leonard Susskind says about this. Watch 1:10:50 where he first give the analogy if the monopol is more fundamental or the electron, and then answers this about strings. video

Comments

Thanks, but the monopole analogy is not the explanation I am looking for. I can understand this in the sense Urs explains between strings and branes and yes I agree. My question was different a less well defined (actually I come to understand it is completely ill defined).