Wiresize required for air conditioner of 1.5 tonne is 2.5 sq mm will work?
2.5mm^2 wire is good for 18A inside a wall, so you are limited by the 15A sockets. A 220V 15A socket can deliver 3.3kW, and even if the voltage drops to 180V it can still do 2.7kW.  Your aircon requires 1.55kW so there is enough power available.

Depending on the type of aircon, it might draw more Volt-Amps than it does Watts. This would happen if it uses a big motor, and has a poor power factor.  Most aircons would be fine, but without looking in the manual for your particular model, it's hard to be sure.

Stabilizers are rarely used in my country, so I can't say much about that part of things, but your 15A sockets cannot supply 4KVA. If the load on the stabiliser stays at 1.5kW, it may be that the stabiliser will always stay below the 2.7kW which is available. If it tries to draw 4KVA from your sockets, there will be problems - either blown fuses, or, if you don't have fuses then a house fire.  Check the manual for the stabiliser to see how it works, and make sure you install 15A fuses somewhere between the wall socket and the stabiliser.

If in doubt, get a qualified electrician in.