String Basics question from an ABJECT ignoramus

[DonFromPgh]

TL;DR Summary

Questions that show my naivete about current string theory

I know this will demonstrate how ignorant I am about the current state of string an brane theory, but I have a question that I don't think I could find the answer in current discussions. Please don't be too harsh.

A string has to come in one of only a few "types":

Closed - the string is connected and forms a loop, with or without knots, as complex as you can imagine.
Infinite - the string stretches from infinity to infinity.
Terminated - the string has endpoints.

The question I have, is, why cannot these three different types of strings produce three types of matter/energy? One of them normal matter, another, dark matter, and the third, some manefestation of dark energy?

I lknow, I know, simplistic, amateuristic naivite from someone who has not learned the intricacies of all of string/brane theory, and has what's probably a question that's already answered in the basics, but inquiring minds would like to know.

 

[Demystifier]

Loosely speaking: closed strings are gravitons, open terminated strings are matter and photons, infinite strings don't exist.

 

[PeroK]

Even if you don't know much about string theory (I certainly don't) you're not obliged to describe yourself in such unflattering terms.

 

[mitchell porter]

A few preliminary comments:

A string with endpoints is called an open string, and the endpoints are attached to branes.

It's often said that a closed string is a graviton, and an open string is a gauge boson (force particle for Yang-Mills fields like electromagnetism or the strong force). This is true in the context of certain forms of string theory. However, e.g. in heterotic string theory, all the strings are closed, including the gauge bosons. Also, that's only discussing strings which are bosons; strings which are fermions, whether open or closed, are matter particles.

If an infinite string is allowed, one should also allow a "semi-infinite" string, which is infinite in one direction but terminates at an endpoint (on a brane) in the other direction. Either way, such a configuration has an infinite energy difference compared to a configuration without such a string (since the string has tension per unit length, and is infinitely long), so "infinite strings" are not quite the same kind of thing as a finite string that can be created with a finite amount of energy.

Instead, an infinite "string" is a permanent fixture of the space-time that contains it - in fact, we would call it a "1-brane". It can vibrate, it can emit and absorb finite strings, but it can't be removed by any process involving a finite amount of energy, because it's infinite. Branes don't have to be infinite, you can have finite branes that come and go just like finite strings, but branes are the objects in string theory (apart from space-time itself) that can be infinitely large, only in that case they are part of the background that defines a particular "vacuum" of string theory.

In this sketch of how strings and branes work in string theory, I'll comment on one more thing: a string can be knotted only in three dimensions of space - in higher dimensions, any "knot" can unravel - and you may be aware that string theory is fundamentally a higher-dimensional theory, although there are ways to make it effectively a lower-dimensional theory. The quantum study of knots is mostly carried out through field theory, via lines of flux.

OK, so there were some basic comments to orient the following discussion. Now onto the application of string theory to physics.

You may also be aware that string theory can describe googols of possible worlds which are all worlds of string, but which differ in their geometry, branes, fluxes, etc. The quest to describe the observable world is all about looking for particular string worlds ("string vacua") which resemble what we see. The reason that people work on string theory is that it does generically produce fermions and Yang-Mills forces and gravity, the challenge is to make it produce those things in the right combination.

So, suppose we indeed want to account for normal matter, dark matter, and dark energy. Normal matter is the particles and fields that we know; the nature of dark matter is unknown except that it doesn't interact electromagnetically and it seems to form relatively inert shells ("haloes") around the galaxies of normal matter; and the nature of dark energy is also unknown except that it needs to be a small homogeneous energy density throughout space.

Just in terms of field theory, normal matter is considered to be described by the quantum fields of the standard model; dark matter by some new quantum fields; and dark energy is usually supposed to be the combined vacuum energy of all these quantum fields (i.e. the energy arising at every point in space, from the quantum fluctuations of these fields in vacuum). In a string theory model, it works the same way, except that you should substitute "string states" for "quantum fields".

But, string theory is flexible, and theorists should be flexible, so let's consider what might be involved in trying to associate "normal matter, dark matter, dark energy" with "open string, closed string, infinite string" in some order.

The closest thing that is coming to mind, is what's called a "braneworld" model. As I mentioned, an "infinite string" would really be part of the background in terms of which the interactions of the "finite strings" are defined; and it would actually be a kind of brane. And there are models in which our apparently 3d world is actually just a 3d brane in a higher-dimensional space (or a 3d overlap between branes that individually have more than 3 dimensions), the matter particles and the non-gravitational forces are open strings attached to that brane, and gravity is due to closed string that temporarily detach from the brane.

In such a model, you would usually have normal matter and dark matter coming from the "open string sector", gravity coming from the "closed string sector", and dark energy coming from the vacuum fluctuations of the brane itself. You could also have a second brane parallel to ours but lying some distance away in the extra dimensions, which has its own open strings attached to it. The matter on that brane can't cross over to our brane, but if it were close enough, we might feel its gravitational influence here, and that could be the dark matter. So that would be a model in which the dark matter is not made of closed strings, but in which the closed strings - because they alone can cross the gap between braneworlds - are the way that we feel the presence of dark matter. This would be a string theory version of what's called a Randall-Sundrum model.

A more exotic possibility following your suggestion, would be if there is no actual dark matter, but rather the observed effects are due to gravity deviating from Newton's law in certain regimes. If such an effect could be produced solely by higher-order quantum effects in the interactions of the closed strings, that really would be a closed-string model of "dark matter".

On the other hand, I didn't find a meaningful way to get dark energy from infinite strings, only from the vacuum fluctuations of an infinite 3-brane. The only truly stringy idea I've had for dark energy is if the acceleration in the universal expansion were somehow due to strings that cross our cosmological horizon. There is another kind of string model, M(atrix) theory, in which the basic variables are 0-branes (point-branes) connected by strings, so maybe one set of 0-branes could pertain to the observable universe, everything we can see within our cosmological horizon, and then we could consider strings between 0-branes that are within the horizon, versus strings between 0-branes inside and outside the horizon. Possibly Susskind is looking at this.

 

[DonFromPgh]

Loosely speaking: closed strings are gravitons, open terminated strings are matter and photons, infinite strings don't exist.

Thanks.