String Field Theory: A Review

As of today, there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings, and type II strings. The construction of these theories requires algebraic ingredients, such as A∞ and L∞ homotopy algebras; geometric ingredients, relevant to the building of moduli spaces of Riemann surfaces and the distribution of picture changing operators; and field-theoretic ingredients, involving two-dimensional CFT’s and BCFT’s and Batalin-Vilkovisky quantization. Applications of string field theory include the description of non-perturbative phenomena such as tachyon condensation and classical solutions and the resolution of a number of ambiguities that bedevil the world-sheet formulation of perturbative string theory. It also allows, given a proper definition of contours of integration for momenta, for a proof of unitarity and a clear understanding of the ultraviolet finiteness of the theory. In this chapter, we review these developments.