Are Strings and Particles in a 1-1 Relationship According to String Theory?

[Jimmy Snyder]

The image I get from reading the popular literature is that, according to string theory, there is a one to one relationship between strings and particles. Another way of saying this is that there are exactly as many strings in the universe as there are particles. The way that the string vibrates determines which species of particle the string is related to. String A vibrates as a proton, while string B vibrates as an electron, etc. Is this too naive? If so, what is the correct view?

 

[dav2008]

I am curious of this as well.

 

[richnfg]

Yes, good topic. In my book, also, it talks about this but doesn't relate any particular vibrations as certain particles or specify how many there are. Would be good if I could get a better understanding too! :)

 

[Javier]

The idea is roughly right: a single type of string can look like particles with different quantum numbers like spin, charge, etc. (However, the proton is a composite particle while a single string should correspond to an elementary particle.) But there are a great number of technical issues to cover before it can be seen that quantum field theory, which is the framework of the Standard Model of particle physics, comes out as an effective description. That is what stringy physics should look like with the limited resolution and power of our "microscopes" (accelerators).

For example, the simplest type of string (embedded in spacetime) gives only particles with integer spin; to get fermions (spin-1/2, etc) the string must, loosely, be embedded in a "superspace" which has commuting and anticommuting coordinates. Also, there are fundamentally two types of string: open | and closed O, which have different particle spectra. And so on...

The underlying idea, though, is always the following:
When the *quantum mechanical* string theory is considered, there are states "|a>" and operators "A" just as in any quantum theory. The different operators A_1, A_2,... of the theory are building blocks, carrying a basic set of quantum numbers; each time you apply an operator to a state such as A_1|a(0)>=|a(01)>, the quantum numbers of the state change (and you say the string is in a different vibrational mode). Each of these states corresponds to what we'd see as a particle with a distinct spin, charge, mass etc. (the extended nature of the string being unobservable due to the limits of our "microscope" accelerators). In this way, acting with the full set of operators in all possible combinations on the "ground state" of the theory, you generate all possible quantum states |a(0)>, |a(01)>, |a(02)>,... of the theory, hopefully including all of the observed particles of the Standard Model.

However, the mass of these "excited states" is quite large and so none of the masses of the *observed* particles can come from these excited strings. That is, generally there are light particles predicted by string theory that we don't see in nature, as well as *infinitely many* very massive states that we wouldn't *expect* to see in the near future. It is the superfluous light states that are troublesome in constructing realistic models.

 

[Dcase]

I have been reading about string theory, most recently about twistor string theory.
I think that I have a minimally basic understanding, but certainly am no expert.

I have these observations and questions:

1 - The helix is an important structure in transmitting information of various types:
- only known structure capable of reproducing and adapting at the cellular gauge
- music theory mathematics [wave and matrix]
- 3D form of Schroedinger equation [and Heisenberg equivalent] in QM
- 3D form of Steinmetz phasor equations in EE AC electricity



2 - Simple and complex harmonic oscillators are known to exist.
Are strings oscillators with specific gauge properties?

If vibrating stings are like these entities, then is gauge the only difference?
If not, what are the differences?

Does gauge theory extend to the planetary, stellar and galactic range of GR / SR?
Or is gauge theory limited to the QM range?



3 - Helicity is emphasized in emphasized in twistor string theory.

Does this refer to the helical trajectories found in mechanics and ballistics?

If so, then should helicity become a dimension like the string dimension used by Borcherds in the proof of Monstrous Moonshine?

If so, does twistor string theory become a subset of Monstrous Moonshine?


4 - Dimension seems to be used in multiple ways by various authors.
The Calabi-Yau manifold has three real and three imaginary axes.
This appears to be treated as six total dimensions in M-theory.
But this appears to be treated as three complex dimensions in twistor string theory.

[VERY SPECULATIVE] - Yet could this not be treated as one spatial dimension if dimension is rigidly defined as “degree of freedom”?

Caspar Wessel in 1797 appeared to have demonstrated the imaginary unit was rotated one unit counterclockwise from the real line - not really a degree of freedom.
One could argue that Wessel thus demonstrated that that the imaginary unit is more ‘invisible’ than imaginary.
Perhaps one could argue that since the real y and z axes are both orthogonal to the real x-axis - that these are really not degrees of freedom.

 

[Jimmy Snyder]

The idea is roughly right

I figured. What I really want to know is where is it not exactly right.

a single type of string

I thought there was only one type of string. What are the different types?

can look like particles

Does this mean that one string can be associated with more than one particle at a time?

Thanks for taking the time to look into this, Javier, but I feel that you have taken this discussion away from the question that I asked. There are some $$10^{80}$$ particles in the universe. Are there the same number of strings? Are they associated with each other one to one?

 

[Javier]

I thought there was only one type of string. What are the different types?


Does this mean that one string can be associated with more than one particle at a time?

Thanks for taking the time to look into this, Javier, but I feel that you have taken this discussion away from the question that I asked. There are some $$10^{80}$$ particles in the universe. Are there the same number of strings? Are they associated with each other one to one?

OK. The confusion here is in the two ways I was using "type of string". In your first sentence above, replace "type of string" by "choice of string model" (there are 5 in the case of superstrings). Once a *model* is chosen, there is then one type of string. Then each string in space looks like a single particle, depending on how it's excited. So there'd be a 1-1 correspondence between elementary particles and strings.

 

[Jimmy Snyder]

So there'd be a 1-1 correspondence between elementary particles and strings.

Got it. Thanks again Javier.