Open string end points, their motion in spacetime

[Spinnor]

I have some questions and refer you to the image below the caption of which states,

"D-branes may be of exceptional importance in the explanation of elementary particles of the Standard Model. However, it still remains to find a solid connection between the M-theory and the Standard Model."

From, http://www.diffusion.ens.fr/vip/pageJ03.html

The string which is identified with a photon above is shown with the ends of the string at different positions on the brane, is there significance to this?

The string ends of an on mass-shell photon must move through space at the speed of light while attached to the brane?

We are told the photon string ends have opposite charge, can we make a connection to this idea and the oscillating nature of an electromagnetic wave?

An electromagnetic wave in free space has equal energy in the electric and magnetic fields. Are there quantities associated with the photon string which represent two forms of energy that are also equally divided?

Can a photon which is off mass shell be included in the image above, is there a representation of it?

Electrons and photons have different spin, does this fact follow from the image above somehow?

Thanks for any help!

 

[Urs Schreiber]

Generally, these pictures serve to enconde basic information about choices of intersecting brane models for readers who already know the mathematics, they cannot explain how string theory works.

To see how a photon mode arises in the open quantum string check out any of the textbooks. Probably you'll like this one:

Luis Ibáñez, Angel Uranga, "String Theory and Particle Physics: An Introduction to String Phenomenology", Cambridge University Press 2012

where the derivation you need is section 3.3.1. The following section then discusses how strings whose endpoints may be attached to several coincident branes yield non-abelian gauge field modes, perturbatively. In the end there is no way except these mathematical formulas to see what's happening. On the other hand, it's really not hard maths, so you should give it a try.

shown with the ends of the string at different positions on the brane, is there significance to this?

Yes. This indicates that it is an "open" string. It is only the open strings which have YM-gauge fields in their massless spectrum (at least without KK-mechanism), the closed string carries the field of gravity and the axion field in its massless spectrum.

We are told the photon string ends have opposite charge, can we make a connection to this idea and the oscillating nature of an electromagnetic wave

No, that's two completely different things.

An electromagnetic wave in free space has equal energy in the electric and magnetic fields. Are there quantities associated with the photon string which represent two forms of energy that are also equally divided?

The massless oscillations of the open string make it look like quanta of the electromagnetic field (the vector potential) and in this way every statement about electromagnetic waves in perturbative QFT is reflected in a corresponding statement about massless excitations of open strings in perturbative string theory.

Can a photon which is off mass shell be included in the image above, is there a representation of it?

The string perturbation series is a straightforward modification of the Feynman perturbation series, and hence where you see off-shell virtual particle lines in Feynman diagrams, there is always the analogous lift to string theory (see here).

Electrons and photons have different spin, does this fact follow from the image above somehow?

Yes, the fermion quanta arise from massless fermionic excitations of the fermionic string (superstring) in analogy to how the gauge field quanta arise from the bosonic massless modes.This is also explained briefly but precisely in that section 3.3. of

Luis Ibáñez, Angel Uranga, "String Theory and Particle Physics: An Introduction to String Phenomenology", Cambridge University Press 2012

 

[mitchell porter]

A few quick thoughts rather than proper answers:

The questions about electromagnetism are interesting but I believe they would be best answered by looking at some intermediate levels of description: classical electrodynamics, then quantum electrodynamics, then the Born-Infeld theory which happens to apply to gauge theories on the brane, and then perturbative string theory (with perhaps an excursion into string field theory if one can find relevant work).

For example, the question about energy in the electric and magnetic fields. First one should understand this in classical terms (energy density, Poynting vector), then try to understand what electric and magnetic field amplitudes are in terms of photon states, then perhaps look at the Poynting vector in Born-Infeld theory and in string theory.

Feynman has a good exposition (which is online) of energy density in classical electrodynamics, including the ambiguity in the definition of energy density and energy flow, and the observation that this could be settled empirically if it were possible to observe the gravitational force due to the electromagnetic energy density. I am not aware if there is a modern way of thinking about this issue (e.g. how does the ambiguity look in different gauges?), but as a matter of theory one could also ask how it works in string theory, which as a theory that includes gravity must imply a particular form of coupling between "electromagnetic field energy" and gravity.

 

[Spinnor]

Thanks Mitchell and Urs! I was trying to work forwards and backwards with the few factoids I have at my disposal with regards to the most "simple" part of Nature, electricity and magnetism. I thought that with the photon string ends being charged and with proper and particular motions in spacetime would yield the 4 polarizations of a photon. I am happy to be corrected .

Mindless work awaits me. Thanks!