Previous article about the topic: Time travel: reality and mythsClosed time-like curves lead to all kinds of problems with causality: no one knows whether you can kill your grandparents before they met and what should happen if you kill them.
Remotely related: 30 neat new hi-res pictures from the LHCHowever, Kurt Gödel has shown that rather mundane distributions of matter have the potential to produce such closed time-like curves because general relativity makes space and time more dynamical than you might think.
But the paradoxes shouldn't exist, should they? That's why in 1992, Stephen Hawking formulated his Chronology Protection Conjecture. In Nature, allowed processes can't produce closed time-like curves, he postulated.
But can we prove such a hypothesis? Do we really know where it comes from? In various supersymmetric theories and vacua, people managed to prove the "specialized" proposition. The proofs always relied in supersymmetry.
But what happens if it's broken?
In the most interesting hep-th paper today,
Joris Raeymaekers (Prague), Dieter Van den Bleeken (Rutgers), Bert Vercnocke (Leuven): Relating chronology protection and unitarity through holography,the authors show that exactly at the point where a dust ball in AdS3 would begin to create closed time-like curves, the unitarity condition "M+1 ≥ J" gets violated.
In other words, there exist no states in the dual CFT that could represent the dust balls capable of producing chronological paradoxes and only arguments based on AdS/CFT correspondence, not those building upon supersymmetry, are needed to see it is the case.