S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
Martingale-observables for dipolar SLE with the Dirichlet boundary condition
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- 학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 2. 김판기.
- 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.