and it doesn't sit well with the folks they leave behind that have to figure out what you were working on and pick up the pieces. It could easily burn a bridge with those folks in the future, and I'm sure someone in your new company would wonder if you'd do that to them someday. But you say you've already spoken with you current management, and maybe they're already expecting it, and have plans to pick up the pieces?

I'm assuming this isn't a case where you are leaving for a direct competitor to your current company. If that were the case, your current company could walk you out right away.