Strings in Space

Abstract

String theory was originally invented to describe hadrons.* Ultimately this idealized mathematical theory of hadrons failed, owing in part to the inability to couple strings to the external local fields, such as the electromagnetic field. The reason for this failure is the infinity of normal mode zero point fluctuations spreading the string over all space [2]. In this chapter we will examine in detail the spatial properties of fundamental strings. We will also speculate on how they compare with the strings of large-N _color gauge theory.^† We will be particularly interested in the following characteristics of the ground state of the fundamental string:

• 1. What is the average size of the spatial region occupied by the string?

• 2. What is the average length of the string?

• 3. Is the string smooth on small scales or does it exhibit rough or fractal-like behavior?

• 4. How densely is space filled with string?