To add a little to this.
The sizing of conductors for general purpose branch circuits have to take into account that they can be over loaded, so it is required to have protection rated at what the conductors can handle under an over load, this is more long term type of over load, But when it comes to motors and A/C units, they already protect the conductors with a built in overload device, and since nothing else should be placed upon this circuit (like a range or a dryer:roll
they will be protected.
So since the conductor is already protected by the overload in the compressor, the conductors can be sized for just fault current, so in essences a 14 AWG conductor will still be protected from a short circuit by a 30 amp breaker because of the available current in a bolted fault will still clear the breaker within the require time, now if the circuit is long then this has to be taken into account as the added resistance can cause a longer tripping time and this can cause conductor damage.
Rule of thumb is wire for the minimum and breaker for the max.