String Field Theory -- A Modern Introduction

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-Universität LMU (winter semesters 2017-2018 and 2018-2019). The current document is the draft of the manuscript published by Springer.

This is a preprint of the following textbook: String Field Theory: A Modern Introduction, authored by Dr. Harold Erbin, 2021, Springer reproduced with permission of Springer. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-65321-7. 318 pages

References in corpus (17)

• Double Field Theory
• Doubled Geometry and T-Folds
• String Field Theory Solution for Any Open String Background
• NS-NS Sector of Closed Superstring Field Theory
• String Field Theory -- A Modern Introduction
• Unitarity of Superstring Field Theory
• Open superstring field theory I: gauge fixing, ghost structure, and propagator
• $A_{\infty }$ structure from the Berkovits formulation of open superstring field theory
• String Perturbation Theory Around Dynamically Shifted Vacuum
• New Covariant Gauges in String Field Theory
• Gauge-invariant observables and marginal deformations in open string field theory
• General Linear Gauges and Amplitudes in Open String Field Theory
• Highly Excited Strings I: Generating Function
• Democratic Superstring Field Theory: Gauge Fixing
• Closed string field theory without the level-matching condition
• A new approach to the LSZ reduction formula
• First-Order Equations of Motion for Heterotic String Field Theory

Cited by in corpus (21)

• String Field Theory -- A Modern Introduction
• Nonperturbative renormalization for the neural network-QFT correspondence
• Bootstrapping closed string field theory
• Hyperbolic string tadpole
• Open string stub as an auxiliary string field
• Boundary terms in string field theory
• Wilsonian effective potentials and closed string field theory
• Characterizing 4-string contact interaction using machine learning
• Finite Entanglement Entropy in String Theory
• Topological aspects of brane fields: solitons and higher-form symmetries
• Topological recursion for hyperbolic string field theory
• Two-Point Superstring Tree Amplitudes Using the Pure Spinor Formalism
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Extra Dimensions and Fuzzy Branes in String-inspired Nonlocal Field Theory
• Covariant phase space and $L_{\infty }$ algebras
• Algebraic Structures In Closed Superstring Field Theory, Homotopy Transfer And Effective Actions
• Symplectic structure in open string field theory III: Electric field
• SL(2, $\mathbb{C}$) quartic vertex for closed string field theory
• On Democratic String Field Theories
• Limiting fluctuations in quantum gravity to diffeomorphisms
• Closed string amplitudes around tachyon vacuum solution in Kaku theory