Are you sure that there is not a vent rising in the wall, behind the sink?
Fixtures do not need a vent to drain. They are self venting. The issue then is the traps will siphon, and you can have odors.
You really do need a vent, and if truly there is not one, a solution not well-loved but acceptable under most codes, is to use an air admittance valve, also called "studor vent"