Two-Point Functions and Boundary States in Boundary Logarithmic Conformal Field Theories

TL;DR

This paper explores boundary logarithmic conformal field theories, focusing on two-point functions, boundary states, and Jordan cell structures, with specific analyses of c_{p,q} theories, free boson models, and the c=-2 triplet model.

Contribution

It provides new solutions for two-point functions, constructs boundary Ishibashi states for Jordan cells, and compares different boundary state constructions in LCFTs.

Findings

Logarithmic solutions of two-point functions found in Coulomb gas picture

Boundary Ishibashi states constructed for rank-2 Jordan cells

Differences between boundary state constructions analyzed and extended

Abstract

Our main aim in this thesis is to address the results and prospects of boundary logarithmic conformal field theories: theories with boundaries that contain the above Jordan cell structure. We have investigated c_{p,q} boundary theory in search of logarithmic theories and have found logarithmic solutions of two-point functions in the context of the Coulomb gas picture. Other two-point functions have also been studied in the free boson construction of BCFT with SU(2)_k symmetry. In addition, we have analyzed and obtained the boundary Ishibashi state for a rank-2 Jordan cell structure [hep-th/0103064]. We have also examined the (generalised) Ishibashi state construction and the symplectic fermion construction at c=-2 for boundary states in the context of the c=-2 triplet model. The differences between two constructions are interpreted, resolved and extended beyond each case.