I went to a lecture a few weeks ago and was told the following:
The world sheet of a closed string is a normal, standing cylinder. The world sheet of an open string is a cylinder on its side. This shows clear duality, therefore unifying gravity with gauge theories, as closed strings are there for gravity and open strings for gauge theories. (Bear in mind this is incredibly simplified as it would be unnecessary for me to go into great detail)
What puzzled me is why the open string produces a world sheet that is a cylinder.
Surely it would produce a 2-dimensional square/rectangle, as this is the shape that's produced when drawing out a world sheet of any horizontally straight line.
The world sheet being a cylinder would mean (according to my intuition) that the string would have to sort of split in 2 (the two strings produced being the same length as the previous lone string) and then rejoin again, producing a cylindrical shape.
This explanation seems extremely non-intuitive, which forces me to question it.
So why is the world sheet of an open string a cylinder as opposed to a 2-dimensional square/rectangle?