New construction home, loose foundation anchor nuts
Yes, they’re suppose to be tight. I suspect they forgot to tighten. I’d hand tighten, plus about a quarter turn. 

The anchor bolts and nuts do two things: 1) keep the house from sliding (moving horizontally), and 2) keeping the house from lifting up (moving vertically. 

I can tell where you live, you don’t have high winds nor do you live in a high seismic area. Where I live we use 3” square and 1/8” thick washers for those anchor bolts and they are 24” oc.  The sole plate would pull through the anchor bolts with those small washers.