|MadSci Network: Physics|
I took a look at the papers you refer to, and they deal with recent developments in string theory, which is a highly theoretical and incompletely understood model for fundamental particle physics. I am an experimental physicist myself, and string theory is way outside my own field of expertise, but from the experimental side:
That having been said, why do you see so much mention of tachyons in string and other quantum field theories (QFTs)?
This is because they are talking about the condensation of tachyonic fields, which are fields in QFTs that have negative squared mass. To my understanding, introducing such fields to a theory are a way to describe an instability that pushes the system towards a potential energy minimum. At this minimum point the tachyonic field no longer has a negative squared mass, and thus becomes stable.
This is important because it allows QFTs to have spontaneuous symmetry breaking, which is necessary to explain the different particle masses and properties of the different forces. The Higgs mechanism is a well-known example of a tachyonic field being used to break, in this case, the electroweak symmetry. Note that while a negative-mass field is used to derive this mechanism, the physical particle (in this case the Higgs boson) has positive mass.
This is a confusing, esoteric subject and I am probably not the best person to explain it, but I hope I have managed (along with the links provided) to help point you in the right direction. Good luck!
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