Summing planar bosonic open strings

In earlier work, planar graphs of massless ϕ3 theory were summed with the help of the light cone world sheet picture and the mean field approximation. In the present article, the same methods are applied to the problem of summing planar bosonic open strings. We find that in the ground state of the system, string boundaries form a condensate on the world sheet, and a new string emerges from this summation. Its slope is always greater than the initial slope, and it remains non-zero even when the initial slope is set equal to zero. If we assume the initial string tends to a field theory in the zero slope limit, this result provides evidence for string formation in field theory.