I am not sure what you are refering to. You absolutely can break Lorentz Invariance in string theory[1]. There is a reason why even some string theory researchers call it the theory of anything.
Wellllll. Despite the title, the paper does not make a claim about string theory. The starting point is the "Witten string field theory" which is a field theory engineered to have properties like string theory. Nothing guarantees that theory is exactly like string theory. In addition, the idea is perturbative in nature, there's no guarantee that perturbative effects are in fact realized in the full quantum theory - exoteric cancellations happen often in field theories with many symmetries. This is two degrees of questionable.
So A) the paper isn't actually about string theory and B) it's not clear that the claim it makes is actually correct for the field theory it supposedly applies to.
Well this is just an early example of the lorentz breaking string theory niche. You can find a lot more. In the short time frame where opera had this supposedly faster than light neutrinos, a lot of papers were published in that regard.
For example you can have string theories that lead to finsler spacetimes, which were used to explain the opera results.
I literally have no idea what our conversation has to do with opera results, or what you think that shows, but just lost all interest in continuing this conversation.
I kind of disagree on your statement about lepton violation. The standard model predicts lepton violating processes (sphalerons). The true symmetry of the standard model is B-L. Of course you are right, that these topological effects will not lead to majorana mass terms.
Well, while sphalerons theoretically break B+L in the non-perturbative regime, they are exponentially suppressed at the energy level of our colliders. At the same time, irrelevant operators that also violate it are suppressed by the GUT scale. So even if you take the minimal Standard Model at face value, you're out of luck finding any sign of the violation either way. But if Neutrinos get Majorana masses, that would be an additional explicit violation at the perturbative level. That would be something we can directly observe, as in neutrinoless double beta decay.
I agree, that neutrinoless double beta decay would be incredibly interesting, but it is very speculative (and depending on the neutrino mass hierarchy not really falsifiable).
My original point was just that lepton number is not a good symmetry as it is broken by rhe chiral anomaly, which is not speculative at all. Of course, the sphaleron effects are negligible in collider settings, but for cosmology they are crucial and might be indirectly observable.
This comparison is not really fair. On the one hand you have the prediction of a scalar excitation with a lot of restrictions (cosmology and naturalness). On the other hand you have a giant framework that can predict or fit almost anything.
Don't get me wrong, I still regard string theory as a big success. It taught us a lot about mathematics and field theories in the last decades.
However the predictive nature is basically non-existant so far.
Nonsense. It can't predict everyone, in particular it won't predict special relativity bring violated.
In addition you haven't addressed the main point here which is that when some people say "can predict" they mean "in principle it can predict" whereas other mean "can predict today with currently available technological means". Regarding the former: yes it can. I already gave the example of one such prediction, but here's another one: all particles niches have stringy modes in their spectra. Regarding the later: maybe, but thats a problem with our technology, not with the theory.
I feel this conservation is going in circles already.
Just because they are not mainstream, you definitely can have lorentz violation in string theory [0]. Spontaneous symmetry breaking can lead to induced finsler geometries, which can basically have multiple light cones (when there was the "faster than light neutrinos" result on the table. Some people used finsler spacetime to explain them).
So you made your prediction only by choosing an axiom.
There is a reason that even some proponents of string theory call it the theory of anything.
I tried to use the extension, but unfortunately i couldn't resolve my problems with it. I always run into errors when i try to execute queries on delta tables.
If you have some knowledge of group theory the 'why' is pretty straight forward.
Quaternions are the generators of SU(2) which is a double covering of SO(3). The latter describes rotations in 3 dimensions. Thus you can express any rotation in 3d with quaternions.
[1] https://inspirehep.net/literature/262241