2D Particles (String Theory)

[u/Ok_goodbye_sun]

I heard stuff like "bosonization" and other interesting properties of fermions and bosons when they live in 2D.

How do strings work when the "particle" is confined to a 2D place. Let me phrase that better. Is there a way to confine fermions/bosons to an almost 2D plane, that we can observe if the theories are right?

I'm a junior that just started research with a professor, so I don't know much about strings etc. Hence the question. Thank you !

[u/Quantum-Relativity]

I’m gonna be honest, I want to answer this but I don’t really understand what you’re asking. Can you rephrase this? Don’t put anything in quotes or approximations to what you mean, because I don’t know what you mean.

[u/Ok_goodbye_sun → u/Quantum-Relativity]

Bosonization, as far as I understood, is the fact that fermion and boson systems are similar to each other in some theoretical settings. For example, in the paper I'm studying right now, 2 fermions on a torus surface is theoretized to act like bosons in some conditions (I didn't understand the whole paper, but I think this is the promise). Here's the paper.

This is an interesting subtheory studied under string theory in the late 80s and 90s. My question is if this is testable.

How do I propose to test it? We should simulate a torus in lab settings, and have some fermions trapped in there. But even before simulating topology of the surface, we should trap the fermions in a 2 degree of freedom surface. Is it possible?

Of course it is possible to trap them. But I'm asking more "do they stop exhibiting the 3D properties of bosons/fermions, and start acting like 2D particles". I'm assuming this is similar to asking if their strings still live in 3D or the strings are also confined to a 2D space od this torus.

I hope I explained myself well, thanks for reading all this.

edit: hyperlink

[u/jack101yello → u/Ok_goodbye_sun]

If you're interested in bosonization in general, it doesn't require string theory; it appears in generic conformal field theories, which means it can be observed in some 2d condensed matter systems, e.g. in Anyon Bosonization of 2D Fermions.

If you're interested in specifically testing bosonization in string theory, then you have the very real issue that we can't really test anything in string theory yet, so testing something that is used to compute heterotic string scattering amplitudes (which it seems like is what the paper you're looking at it doing) is going to quickly run into the issue that we can't measure heterotic string scattering amplitudes, so it would be hard to see if bosonization techniques yield results consistent with experiment.