String Field Theory: A Review

TL;DR

This review discusses the development of consistent, gauge-invariant string field theories for all string types, highlighting their algebraic, geometric, and field-theoretic foundations, and their applications in non-perturbative phenomena and resolving ambiguities.

Contribution

It provides a comprehensive overview of the algebraic, geometric, and field-theoretic ingredients used in constructing string field theories and their applications.

Findings

Unified framework for various string theories

Resolution of ambiguities in perturbative string theory

Demonstration of unitarity and ultraviolet finiteness

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.