That requires the existence of exotic matter, something that really isn't known to exist at all, and it'd be pretty surprising if it did. Pretty much all FTL schemes require some exotic thing that's unlikely to actually be feasible in our universe.
The bending of space is possible though. We could figure out how to bend space in a different way. Think about it, alchemists were trying to figure out how to turn lead into gold. We now know how to transmute an element into gold, although not economically. Science is till pretty young. I wouldn't rule out something similar to the Alcubierre Drive for space travel.