Summing Planar Bosonic Strings

TL;DR

This paper extends previous methods to sum planar bosonic open strings, revealing a string condensate on the world sheet and the emergence of a new, larger-slope string, supporting string formation from field theory.

Contribution

It applies light cone world sheet and mean field techniques to bosonic strings, demonstrating string condensate formation and emergent strings with increased slope.

Findings

String boundaries form a condensate on the world sheet.

A new string with greater slope emerges from the condensate.

The emergent string's slope remains non-zero even when initial slope is zero.

Abstract

In earlier work, planar graphs of massless phi^3 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 that the initial string tends to some field theory in the zero slope limit, this result provides evidence for string formation in field theory.