[论文解读] String Field Theory -- A Modern Introduction

Harold Erbin|arXiv (Cornell University)|Jan 4, 2023

Computational Physics and Python Applications被引用 12

一句话总结

一本全面的教科书，介绍封闭玻色字符串场论、BRST量子化、非在壳振幅，以及一致性属性，并扩展到超弦和背景独立性。

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.

研究动机与目标

• 提供一个自包含、概念驱动的弦场论（SFT）入门，聚焦于封闭的玻色情形。
• 将世界sheet共形场论、BRST量子化和非在壳弦振幅，桥接到弦的场论表述。
• 构建封闭玻色SFT并评估其一致性属性（背景独立性、单位性、交叉对称性）。
• 解释该框架如何推广到超弦，并强调与SFT相关的关键发展。

提出的方法

• 回顾世界sheet理论基礎（路径积分、CFT、BRST量子化）。
• 介绍非在壳弦振幅，并从费曼图视角提取SFT构建块。
• 构建封闭字符串场论并推导其动力学项、传播子和相互作用。
• 讨论BV形式、1PI理论，以及在封闭与开放字符串背景下的规范固定。
• 将该框架推广到超弦与动量空间SFT。
• 提供详细的约定、附录，以及系统性的教学习导以建立直觉。

实验结果

研究问题

• RQ1 封闭玻色弦理论如何作为一致场论来表述？
• RQ2 支撑SFT的基本BRST与BV结构是什么？
• RQ3 非在壳振幅如何产生，以及它们如何被编码在弦场作用中？
• RQ4 在SFT中可以建立哪些一致性证明（背景独立性、健壮性、交叉对称性）？
• RQ5 SFT框架如何扩展到超弦和动量空间表述？

主要发现

• 提出一个自包含的封闭玻色SFT构造，明确讨论其动能项、传播子和相互作用顶点。
• 发展BRST量子化及其同调，用以在SFT框架内识别物理态。
• 分析非在壳弦振幅及其与世界sheet拓扑的关系，给出SFT构建块的费曼图解释。
• 一致性属性如背景独立性、单位性和交叉对称性在SFT概念中被概述并奠基。
• 书中讨论开放字符串、BV形式、1PI理论，以及超弦和动量空间表述的扩展。