String Field Theory: A Review

Abstract

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 require algebraic ingredients, such as $A_{\infty }$ and $L_{\infty }$ 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 article we review these developments.

172 pages, 22 figures. Expanded version of a review for "Handbook of Quantum Gravity", eds. C. Bambi, L. Modesto and I.Shapiro. New version with very minor changes and a few extra references