An interesting issue came up over on one of the Usenet groups
There is a Sea Breeze mini split air conditioner that has an installation manual that says it should be connected with 6 gauge copper. The label says "minimum circuit ampacity" is 26 amps. So who do you believe? The breaker size is 50a. http://www.irproducts.biz/documents/SB-NewMultiZone.pdf
I have 2 of these mini splits and one the inside units runs on low voltage that could be run with bell wire Spec'ed as thermostat cable. It is a very small load (a little fan and an electronic board). The other uses line voltage but just at a few amps.
The conductors going to each inside unit only carry the current to that unit. That is why they can be #14. As for the outside unit, that is specified on the label and you have to trust the engineer who computed it.