For heavy duty, 60 Amps power is reliable. Better to use 10 gauge wire for 230V AC compressor to control the motor and avoid damage during low voltage and lightning.
Depending upon your location, the wire guage required to meet local electrical code will vary. In most cases, 12-gauge wire meets electrical code, however you need to check with your local building code authority to ensure that the wiring is both safe and up-to-code.
It depends on the amount of current going to the compressor. If you are using 40 amps, then you will need #8 AWG wire (copper). For 50 amps, you will need #6. Less than 40 amps, #10 will work.
The manufacturer recommends the actual current protection that is required for their particular unit. The wire size changes with the size or capacity of the air conditioner. The National Electric Code dictates the wire size based on current draw and length of the run. Consult a licensed qualified electrician.