No, they don't.
The general rule of thumb is that spells (and all rules) do exactly what they say they do.
Beware of claims that a rule does something mentioned nowhere in that rule or elsewhere in the core books. There aren't secret rules.
Jeremy Crawford - Voice of Official Rulings for WotC
Arcane Lock says...
You touch a closed door, window, gate, chest, or other entryway, and it becomes locked for the duration. You and the creatures you designate when you cast this spell can open the object normally. You can also set a password that, when spoken within 5 feet of the object, suppresses this spell for 1 minute. Otherwise, it is impassable until it is broken or the spell is dispelled or suppressed. Casting knock on the object suppresses arcane lock for 10 minutes.
While affected by this spell, the object is more difficult to break or force open; the DC to break it or pick any locks on it increases by 10.
Arcane Lock does not specify that the caster is aware if the spell is broken. Therefore, they are not. If they were notified, it would say so.
If you want to be notified of an intrusion, that's what the Alarm spell is for.
For further reading on the 'Spells do what they say', then see here