Is there a wire between starter and alternator?

Yes, there is a wire between the starter and the alternator. This wire is called the "charge wire" or "alternator field wire". It carries a small amount of current from the starter to the alternator, which is used to excite the alternator's field windings and generate electricity. The charge wire is typically a small gauge wire, and it is usually connected to the "S" terminal on the alternator.