This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin.
Part I reviews string field theory from the point of view of homotopy algebras, including A-infinity algebras, loop homotopy (quantum L-infinity) and IBL-infinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory.
Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory.
Author(s): Martin Doubek, Branislav Jurčo, Martin Markl, Ivo Sachs
Series: Lecture Notes in Physics, 973
Publisher: Springer
Year: 2021
Language: English
Pages: 221
City: Cham
Preface
Contents
About the Authors
1 Introduction
Part I Physics Preliminaries
2 Relativistic Point Particle
2.1 BV Action for the Point Particle
2.2 Scattering Matrix and Minimal Model
2.3 Summary, Comments, and Remarks Towards Part II
Further Reading
3 String Theory
3.1 Closed Strings
3.2 Interactions
3.3 Decomposition of the Moduli Space
3.4 Measure, Vertices, and BV Action
3.5 Algebraic Structure
3.6 Coalgebra Description
3.7 Uniqueness and Background Independence
3.8 Summary, Comments, and Remarks Towards Part II
Further Reading
4 Open and Closed Strings
4.1 World-Sheets with Boundaries
4.2 Open String
4.3 Summary, Comments, and Remarks Towards Part II
Further Reading
5 Open-Closed BV Equation
5.1 Open-Closed BV Action
5.2 Quantum Open-Closed Homotopy Algebra
5.3 Summary, Comment, and Remarks Towards Part II
Further Reading
Part II Mathematical Interpretation
Conventions Used in This Part
Reference
6 Operads
6.1 Cyclic Operads
6.2 Non-Σ Cyclic Operads
6.3 Operad Algebras
6.4 Modular Operads
6.5 Odd Modular Operads
References
7 Feynman Transform of a Modular Operad
7.1 Modules and Derivations
7.2 Feynman Transform
References
8 Structures Relevant to Physics
8.1 BV Algebras and the Master Equation
8.2 Loop Homotopy Algebras
8.3 IBL∞-algebras
8.4 Comments and Remarks Related to Part I
References
Index
