> Without the use of adhesives of any kind

Levitation? ;)

You probably need to pass the wire through something rigid (tube, trim...) so it doesn't flip-flop around, then attach both ends of this rigid "thing" to what you have at each end. How you do it without adhesive (and I presume without nails) depends on what you have there. You might twist a coat hanger into a hook if there's a door frame at one end, you might just use a paper weight if it's a corner or recess that doesn't tend to get kicked. You'll have to improvise with the situation.