Harold Erbin - String Field Theory; Modern Introduction

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This book grew up from lectures delivered within the Elite Master Program Theoretical and Mathematical Physics from the Ludwig-Maximilians-Universitt during the winter semesters 20172018 and 20182019.

The main focus of this book is the closed bosonic string field theory (SFT). While there are many resources available for the open bosonic SFT, a single review [2] has been written since the final construction of the bosonic closed SFT by Zwiebach [5]. For this reason, it makes sense to provide a modern and extensive study. Moreover, the usual approach to open SFT focuses on the cubic theory, which is so special that it is difficult to generalize the techniques to other SFTs. Finally, closed strings are arguably more fundamental than open strings because they are always present since they describe gravity, which further motivates my choice. However, the reader should not take this focus as denying the major achievements and the beauty of the open SFT; reading this book should provide most of the tools needed to feel comfortable also with this theory.

While part of the original goal of SFT is to provide a non-perturbative definition of string theory and to address important questions such as classifying consistent string backgrounds or understanding dualities, no progress on this front has been achieved so far. Hence, there is still much to understand, and the recent surge of developments provides a new chance to deepen our understanding of closed SFT. For example, several consistency properties of string theory have been proven rigorously using SFT. Moreover, the recent construction of the openclosed superstring field theory [3] together with earlier works [1, 46] shows that all types of string theories can be recast as a SFT. This is why, I believe, it is a good time to provide a complete book on SFT.

The goal of this book is to offer a self-contained description of SFT and all the tools necessary to build it. The emphasis is on describing the concepts behind SFT and to make the reader build intuitions on what it means. For this reason, there are relatively few applications.

The reader is assumed to have some knowledge of QFT and a basic knowledge of CFT and string theory (classical string, NambuGoto action, light-cone and old-covariant quantizations).

The text is organized on three levels: the main content (augmented with examples), computations and remarks. The latter two levels can be omitted in a first lecture. The examples, computations and remarks are clearly separated from the text (respectively, by a half-box on the left and bottom, by a vertical line on the left and by italics) to help the navigation.

Many computations have been set aside from the main text to avoid breaking the flow and to provide the reader with the opportunity to check by themself first. In some occasions, computations are postponed well below the corresponding formula to gather similar computations or to avoid breaking an argument. While the derivations contain more details than usual textbooks and may look pedantic to the expert, I think it is useful for students and newcomers to have complete references where to check each step. This is even more the case when there are many different conventions in the literature. The remarks are not directly relevant to the core of the text, but they make connections with other parts or topics. The goal is to broaden the perspectives of the main text.