Open Strings, D-Branes, and Conservation of Energy

[Keys]

Can someone please explain to me why string theories with open strings must also have closed strings? I've read it is due to conservation of energy, an open string not attached to a closed string will lose it's energy off an end. Does this mean all D-branes must be made from closed strings? I can easily imagine open strings attached to each other in a manner which does not allow loose ends and doesn't require closed strings.

 

[Demystifier]

Can someone please explain to me why string theories with open strings must also have closed strings?

An easy (though far from rigorous) way to see this is as follows:
A one-loop open-string diagram is topologically the same as a tree closed-string diagram. Try to convince yourself by drawing it!

 

[Keys]

OK, if they look the same, then they are considered equivalent? What's the point in specifying then? This leads to my 2nd question, if a one loop open string is attached to a d-brane, I've read it cannot be detached. But if we can just relabel it a tree closed string, then it is detachable? Thanks.