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Non-perturbative Approaches to Conformal Field Theory : 등각장론의 비섭동적인 접근 방법
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이수종 | - |
| dc.contributor.author | 배진범 | - |
| dc.date.accessioned | 2017-07-19T06:08:05Z | - |
| dc.date.available | 2017-07-19T06:08:05Z | - |
| dc.date.issued | 2015-08 | - |
| dc.identifier.other | 000000056948 | - |
| dc.identifier.uri | http://dcollection.snu.ac.kr:80/jsp/common/DcLoOrgPer.jsp?sItemId=000000056948 | - |
| dc.description | 학위논문(박사)--서울대학교 대학원 :자연과학대학 물리·천문학부,2015. 8. 이수종. | - |
| dc.description.abstract | The goal of this thesis is suggesting diverse method of analysing conformal field theory which related to string theory/higher spin theory via AdS/CFT correspondence. In this thesis, we focus on two specific objects in conformal field theory : 4-point correlation function in O(N) vector model and polygonal Wilson loop expectation value in 3D N=6 superconformal field theory.
The first part of this thesis devoted to non-perturbative analysis of conformal field theory. Based on unitarity and crossing symmetry of 4-point correlation function, conformal bootstrap program enables pick up UV and IR fixed point of O(N) symmetric theory for 2 The polygonal Wilson loop expectation value is intensively discussed in second part of this thesis. We computed hexagonal two-loop Polygonal Wilson loop expectation value in 3D N=6 superconformal field theory and showed structurewise similiarity with that of N=4 super Yang-Mills theory. Also, we focused on its universal behavior under collinear-soft limit. Based on this observation, we constructed structure of polygonal Wilson loop for arbitrary number of edges at two-loop order. At circular limit, the result agrees to circular Wilson loop expectation value. | - |
| dc.description.abstract | 이 논문에서는 등각장론에서 정의된 다양한 물리량들을 통해 섭동적 혹은 비섭동적인 등각장론의 성질을 규명한다. 첫째로, 5차원 등각장론에서 정의된 4점함수에 유니테리 성질 및 교차 대칭성을 통한 제한조건을 분석하여 UV 고정점에 해당하는 등각장론이 존재함을 논의하였다. 다양한 차원에서 이 방법은 비섭동적인 상호작용하는 이론을 통해 규명할 수 있는 임계지수를 성공적으로 유도해낼 수 있음이 확인되었다.
둘째로, 초대칭을 가지는 3차원 ABJM 이론에서 경로가 첨점을 가지는 경우에 해당하는 윌슨고리를 조사함으로써 해당 이론의 성질을 규명하고자 하였다. 특히, 윌슨고리의 특정한 극한을 조사함으로써 6각형 윌슨고리의 결과로부터 n각형 윌슨고리의 결과를 얻어낼 수 있는 방법을 제시한다. 이 결과는 n이 무한대로 가는 극한에서 초대칭 국소화를 통해 얻어낸 비섭동적인 결과와 잘 일치한다는 것이 확인되었다. | - |
| dc.description.tableofcontents | I. Intro - Symmetries in Relativistic Quantum Physics
1.1 The Conformal Group 1.2 Phase Transition in condensed matter theory 1.3 Renormalization group flow 1.4 AdS/CFT correspondence 1.5 Observables in conformal field theory II. Correlation function in conformal field theory 2.1 General structure of correlation function 2.2 Radial Representation of Conformal Block 2.3 Conformal Bootstrap Method 2.3.1 e-expansion 2.3.2 Bootstrapping 3 dimensional critical theory 2.4 Non-trivial fixed point in 5 Dimension 2.4.1 Hubbard-Stratonovich transformation 2.4.2 5-dimesional conformal bootstrap : one-parameter result 2.4.3 5-dimesional conformal bootstrap : two-parameter result 2.4.4 Bootstrap Results III. Interlude : Scattering amplitude versus Polygonal Wilson loop in N = 4 SYM 3.1 Gluon Scattering Amplitude in N = 4 SYM 3.2 Polygonal Wilson loop expectation value in N = 4 SYM IV. Polygonal Wilson loop in ABJM theory 4.1 Main Results 4.2 Light-like Polygon Wilson loop in ABJM Theory 4.2.1 ABJM Theory 4.2.2 Previous Results 4.3 Hexagon Wilson Loops at Two Loops 4.3.1 Matter Contribution 4.3.2 Gauge Boson Ladder diagram 4.3.3 Triple-Vertex Diagram 4.3.4 Wilson Loop of the Pure Chern-Simons Theory 4.4 Euclid, Mandelstam and Gram 4.4.1 Moduli Space of Lightlike Polygon 4.4.2 Euclidean Configuration 4.4.3 Moduli Space of Conformal Lightlike Polygon 4.5 The Hexagon Remainder Function 4.5.1 Remainder Function in N = 4 Super Yang-Mills Theory 4.5.2 Scalar Invariants and Gram Sub-Determinant Conditions 4.5.3 Special Shapes and Asymptotic Limits 4.6 Lightlike Factorization and Antenna Function 4.6.1 Infrared Factorization in Gauge Theories 4.6.2 Lightlike Factorization of Wilson Loop 4.7 Antenna Function for the ABJM Wilson Loops 4.7.1 Moduli Space of Lightlike Polygon Factorization 4.7.2 Matter Contribution to Antenna Function 4.7.3 Chern-Simons Contribution to Antenna function 4.7.4 ABJM Antenna Function 4.8 Recursion Relations and ABJM Wilson Loop Expecation Value 4.9 Circular Wilson Loop V. Outro Bibliography Appendices I. Appendix A : Notation, Convention and Feynman Rules II. Appendix B : Self energy of gauge field III. Appendix C : Mellin-Barnes transformation IV. Appendix D : Ladder Diagrams V. Appendix E : Dimensional Redection Scheme VI. Appendix F : Expressions for vertex diagrams VII. Appendix G : Expressions for I521 and I541 VIII.Appendix H : Gram determinant constraint for conformal cross ratio | - |
| dc.format.extent | vi, 136 | - |
| dc.language.iso | eng | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject | String theory, Conformal Field Theory, Conformal Bootstrap, Polygonal Wilson loop, AdS/CFT | - |
| dc.subject.ddc | 523 | - |
| dc.title | Non-perturbative Approaches to Conformal Field Theory | - |
| dc.title.alternative | 등각장론의 비섭동적인 접근 방법 | - |
| dc.type | Thesis | - |
| dc.type | Dissertation | - |
| dc.contributor.AlternativeAuthor | Jin-Beom Bae | - |
| dc.contributor.department | 자연과학대학 물리·천문학부 | - |
| dc.description.degree | Doctor | - |
| dc.date.awarded | 2015-08 | - |
| dc.identifier.holdings | 000000000023▲000000000025▲000000056948▲ | - |
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