What's the best way to attach new basement walls to the floor without drilling into the slab?

The most common and secure way to attach a bottom plate to a concrete slab is with concrete screws or a powder-actuated nailer. If drilling is truly not an option, a high-strength polyurethane construction adhesive can be used for *non-load-bearing* walls, but this is less common and offers less stability. The bigger issue here is often building code compliance; many jurisdictions require mechanical fasteners for structural integrity and seismic resistance. Skipping these could lead to an unsafe structure or require costly rework. Always check with your local building department first.