Higher Spin Gauge Theory and Related Issues

학위논문(박사)--서울대학교 대학원 :자연과학대학 물리·천문학부,2016. 8. 이수종.Since the very earlier days of quantum eld theory, the existence of the massless higher spin has been known. However, there were various obstacles to reach an interesting higher spin gauge theory. The most of all na ̈ıve try for introducing interactions between a massless higher spins and another elds had failed. Because the higher spin gauge symmetry is not conserved at all. It was hard to nd the consistent interaction of higher spin gauge theory. In recent years, ourished achievements have been made. In this thesis, we try to review about obstacles and achievements, and summarised our own effort to nd new interacting theories.양자 장론의 발전 초기 단계에서 부터 질량이 없고 고차 스핀을 가지는 입자의 존재에 대해서 알려져 있었다. 하지만 흥미로운 이론을 찾기가 어려웠는데, 그 이유는 다른 입자와 상호 작용 을 하는 이론을 구성하는데 어려움이 있었기 때문이다. 최근에 다양한 이론들이 제시되었다. 이 논문에서는 여러가지 어려움들과 최근의 발전 상황을 소개하고, 새로운 상호작용하는 이론을 찾 으려는 저자의 노력에 대해 정리할 것이다.Chapter 1. Motivation 1 Chapter 2. Introduction to Higher Spin Gauge Theory I: Metric-likeFormalism 3 2.1 Higher Spin Fields: FlatSpace 4 2.1.1 Massive Higher Spin Lagrangian: FlatSpace 4 2.1.2 Massless Higher Spin Lagrangian: Flat Space 8 2.2 Higher Spin Fields:(Anti-)deSitterSpace 12 2.2.1 Long and Short Higher Spin Representation: AdS Space 12 2.2.2 Massive and Massless Higher Spin Field on (A)dS 17 2.3 Partially Masselss Fields on (Anti-) de Sitter Space 19 2.3.1 Gauge Symmetry 20 2.3.2 Stueckelberg Trick 23 2.3.3 First Derivative Description in Three Dimension 25 Chapter 3.Introduction to Higher Spin Gauge Theory II:Frame-likeFormalism 27 3.1 Unfolded Equations and Vasiliev System 27 3.1.1 Vasiliev system in four dimension 27 3.2 Analysis of Unfolded Equations 31 3.2.1 Decomposition of Form into Irreducible Components 32 3.2.2 Analysis of Equation: One-formSector 34 3.2.3 Analysis of Equation: Zero-formSector 38 Chapter 4. (Anti-) de Sitter Space Waveguide 41 4.1 Flat Space Waveguide and Boundary Conditions 42 4.2 Waveguide in Anti-de Sitter Space 47 4.3 Waveguide Spectrum of Spin-1Field 49 4.3.1 Mode function structure of spin-1 waveguide 49 4.3.2 Waveguide boundary conditions for spin-1 eld 51 4.4 Waveguide Spectrum of Spin-2Field 53 4.4.1 Mode function structure of spin-2 waveguide 53 4.4.2 Waveguide boundary conditions for spin-2 eld 57 4.5 Waveguide Spectrum of Spin-3Field 59 Chapter 5. (Anti-)de Sitter Space Higher-SpinWaveguide 63 5.1 Higher-Derivative Boundary Condition 63 5.1.1 Simple Example: Vibrating String System 64 5.1.2 Spin-2 Waveguide with Higher-Derivative Boundary Conditions 67 5.2 Waveguide Spectrum of Spin-s Field 71 5.2.1 Dimensional reduction of gauge transformation 72 5.2.2 Waveguide boundary conditions for spin-s eld 73 5.2.3 Decompactication limit: α→π/2 77 5.3 Toward Interaction 78 5.3.1 Gauge Symmetries in (A)dS Waveguide: Hihger Spin Generalization 79 5.3.2 Reduced higher spin algebra and Chern-Simon equation: d=2 case 81 5.4 Comment 82 Chapter 6. ColoredGravity 87 6.1 Introduction 87 6.2 No-Go Theorem on MultipleSpin-TwoTheory 89 6.3 Color-Decorated (A)dS3 Gravity: Chern-Simons Formulation 90 6.3.1 Color-Decorated Chern-SimonsGravity 90 6.3.2 Basis of Algebra 92 6.4 Color-Decorated (A)dS3 Gravity: Metric Formulation 94 6.4.1 Colored Gravity around Singlet Vacuum 95 6.4.2 First-orderDescription 97 6.4.3 Second-order Description 97 6.5 Classical Vacua of Colored Gravity 98 6.5.1 Identification of Vacuum Solutions 98 6.5.2 N =3 Example and Linearized Spectrum 101 6.6 Colored Gravity around Rainbow Vacua 104 6.6.1 Decomposition of Algebra Revisited 104 6.6.2 ColoredGravity around Non-Singlet Vacua 107 6.6.3 Partially Massless Spectrum Associated with Broken Color Symmetry 108 6.7 Discussions 110 Chapter 7. ColoredHigherSpin 113 7.1 Introduction 113 7.2 Color Decoration of Higher-Spin(A)dS3 Gravity 114 7.2.1 Color Decoration 114 7.2.2 Color-Decorated (A)dS3 Higher-Spin Theory 115 7.3 Color Symmetry Breaking and Rainbow Vacua in General Dimensions 117 7.4 Metric Formulation 120 7.4.1 Decomposition of Associative Algebra 120 7.4.2 Action in Metric Formulation 122 7.5 Mass Spectrum of the Broken Color Symmetries 125 7.5.1 General Structure 125 7.5.2 Example: gl3⊕gl3 126 7.6 Partially-Massless Fields in ThreeDimensions 127 7.7 Discussions 130 Chapter 8. Conclusion 133 Appendices 135 Chapter A. AdS space and related conventions 137 Chapter B. Verma module and partailly massless(PM) field 139 Chapter C. Reduction Method from(A)dS_{d+k} to(A)dS_d 141 Bibliography 143 초록 155Docto