Geometry of String Space and String Field Theory

Abstract

The impressive recent progress in string theory [1] has taken place for the most part at the level of the first quantized formalism, while the formulation in the language of field theory is far less understood. In a second quantized, field theoretic treatment, the fundamental object is the string field Φ[X], which is a functional of the string configuration x ^μ (σ) becoming, upon quantization, an operator creating a string in that configuration. Formally, the classical theory will be defined by an action given in terms of a Feynman-type path integral of the form

$$ Phi ] = \int {D{x^\mu }(\sigma )L[\Phi ,\delta \Phi /\delta x]} $$

((1))

while the quantum theory is obtained from the generating functional

$$ Z = \int {D\Phi [X]} {e^{iS}} $$

((2))