My new project

Uugh, ok the shop called and got my new alternator in so I picked it up and even had them bench test it first and it put out 13.8 volts and passed no problem.
I installed it as I planned and ran a jumper from the alternator large post to the starter relay large post and started it. It runs fine but no matter what I do it wont show more than 12.3 volts at the battery when I rev it up. Also as soon as I disconnect the battery terminal on the battery it dies immediately.
If the battery supplies power through starter relay just fine and the alternator is wires directly to the starter relay..shouldn't it stay running if I disconnect the battery?