First of all, why are there so many researches to find Lorentz violation? Are there some models of (super-)string theory that include Lorentz violation at some scale?
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An arbitrary string theory doesn't need to break Lorentz symmetry, however some particular string theories can break it. Looking for Lorentz violation is a way to test these particular string theories that can break (spontaneously) Lorentz symmetry. Other exotic theories such as non-commutative field theories and loop-quantum gravity have also been associated with Lorentz violation. Presently is impossible to probe directly gravity at the quantum level. If you want to probe gravity at the quantum level you need to look for indirect methods like looking for exotic signals and a breaking of Lorentz symmetry is one of these exotic signals.
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