Undergrad String theory and Lorentz invariance - 10D vs. 4D....

[asimov42]

Hi all,

Clarification question: I've read that string theory is manifestly Lorentz invariant - however, I'm confused about this being true in 4D spacetime or in the full 10D setting of the theory (well, one version anyway). At some point I'd also read in a paper that 4D Lorentz invariance necessarily breaks Lorentz invariance in 10D ... however, I've misplaced the reference, unfortunately.

If Lorentz invariance in 10D is not satisfied, doesn't this have serious implications? (even if those dimensions are compactified) Or from a GR perspective, does one only care about the 4 extended spacetime dimensions?

 

[asimov42]

And a follow up: if we were somehow able to achieve the required energies to probe the curled up dimensions with a test particle (say a proton), what would one expect to observe, to actually verify the existence of the extra dimensions (I've been unable to find info on this).

Thanks.

 

[asimov42]

Perhaps there's a better way I could ask the question? If in the compactified 6 dimensions, Lorentz invariance is not satisfied, what effects would this have? I'd appreciate any input.

 

[fresh_42]

Well, I'm far from being someone to answer your question. In fact I find it interesting myself, at least how the two concepts match at all, or don't. However, a quick Google search gave me these:

https://en.wikipedia.org/wiki/Lorentz_invariance_in_non-critical_string_theory
http://www.worldscientific.com/doi/pdf/10.1142/S2010194514602749
https://arxiv.org/abs/hep-th/9906003
https://arxiv.org/abs/0708.2250

 

[asimov42]

Thanks @fresh_42. Going to back my second question:

And a follow up: if we were somehow able to achieve the required energies to probe the curled up dimensions with a test particle (say a proton), what would one expect to observe, to actually verify the existence of the extra dimensions (I've been unable to find info on this).

So we accelerate the proton to the point where it acquires sufficient momentum to 'move' in the curled up space - what do we observe (in our particle accelerator)? Simply a massive particle that stops moving in 3D? (because a momentum change to the 6 curled up dimensions would be unobservable) ... that is, what would one expect to happen to the proton at the exact point where it gained sufficient momentum?