String Field Theory

Abstract

This book provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far due to the exceptional properties of two-dimensional theories, it becomes cumbersome for some questions or even fails at a more fundamental level. These motivations have led to the development of SFT, a description of string theory using the field theory formalism (second-quantization). As a field theory, SFT provides a rigorous and constructive formulation of string theory. The main objective is to construct the closed bosonic SFT and to explain how to assess the consistency of string theory with it. The accent is put on providing the reader with the foundations, conceptual understanding and intuition of what SFT is. After reading this book, they should be able to study the applications from the literature. The book is organized in two parts. The first part reviews the topics of the worldsheet theory that are necessary to build SFT (worldsheet path integral, CFT and BRST quantization). The second part starts by introducing general concepts of SFT from the BRST quantization. Then, it introduces off-shell string amplitudes before providing a Feynman diagrams interpretation from which the building blocks of SFT are extracted. After constructing the closed SFT, it is used to outline the proofs of several important consistency properties, such as background independence, unitarity and crossing symmetry. Finally, the generalization to the superstring is also discussed. This book grew up from lecture notes for a course given at the Ludwig-Maximilians-Universit\"at LMU (winter semesters 2017-2018 and 2018-2019). The current document is the draft of the manuscript published by Springer.