First let me say, I don't know that much about long guns, but seems like I read somewhere that with a certain type receiver a AR-15 is considered a pistol. So if that is the case you could carry it with your permit.
With all due respect to any that may read this, there are several LEO's that aren't 100% familiar with the carry and gun laws. Although I admit this is getting better. So would be hard to say what would happen if you were stopped by one.
Just to clarify in TN you can carry any "handgun(s)" with your permit, but it does not cover long guns or other weapons as in some states.