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Martingale-observables for dipolar SLE with the Dirichlet boundary condition
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 김판기 | - |
| dc.contributor.author | 탁희준 | - |
| dc.date.accessioned | 2018-05-28T17:11:58Z | - |
| dc.date.available | 2018-05-28T17:11:58Z | - |
| dc.date.issued | 2018-02 | - |
| dc.identifier.other | 000000150484 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/141145 | - |
| dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 2. 김판기. | - |
| dc.description.abstract | In this thesis, we study a version of dipolar conformal field theory based on the central charge modification of the Gaussian free field with the Dirich- let boundary condition. We prove that correlation functions of certain fam- ily of fields in this theory under the insertion of the boundary condition changing operator are martingale-observables for dipolar SLE. We adopt and modify definitions and basic properties developed in the study of a ver- sion of chordal conformal field theory to implement this version of dipolar conformal field theory. Using techniques in a dipolar conformal field theory, we prove the restriction property of dipolar SLE(8/3), Friedrich-Werners formula in the dipolar case and the Cardy-Zhan observables. | - |
| dc.description.tableofcontents | 1 Introduction 1
2 Main results 4 2.1 Dipolar SLE martingale-observables 4 2.2 A dipolar CFT 6 2.3 Boundary condition changing operators and rooted vertex fields 9 2.4 Examples of martingale-observables 10 3 Basic properties of conformal Fock space fields 12 3.1 Gaussian free field on simply connected domain 12 3.2 Fock space correlation functionals 13 3.3 Fock space fields 15 3.4 Operator product expansion 16 3.5 Conformal Fock space fields 18 3.6 Stress tensor 20 3.7 Virasoro field 22 4 Dipolar CFT 24 4.1 Central charge modification 24 4.2 Ward's functionals and Ward's identities 26 4.3 Ward's equations in the upper half-plane 29 5 Vertex fields 31 5.1 Formal fields 31 5.2 Multi-vertex fields 33 5.3 Coulomb gas correlation functions 36 5.4 Rooted multi-vertex fields 41 5.5 Ward's identity and equation for rooted multi-vertex fields 44 5.6 Level two degeneracy equations 47 6 Connection between dipolar SLE and CFT 49 6.1 Boundary condition changing operator 49 6.2 BPZ-Cardy equations 51 6.3 Dipolar SLE martingale-observables 52 6.4 The restriction property 54 7 Vertex observables 62 7.1 Rooted Multi-vertex fields 62 7.2 Cardy-Zhan observables 65 | - |
| dc.format | application/pdf | - |
| dc.format.extent | 4544116 bytes | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | en | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject | Dipolar conformal field theory | - |
| dc.subject | Dipolar SLE | - |
| dc.subject | martingale-observables | - |
| dc.subject.ddc | 510 | - |
| dc.title | Martingale-observables for dipolar SLE with the Dirichlet boundary condition | - |
| dc.type | Thesis | - |
| dc.description.degree | Doctor | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2018-02 | - |
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