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

Amongst conformal field theories, there exist logarithmic conformal field theories such as cp,1 models, various WZNW models, and a large variety of statistical models. It is well known that these theories generally contain a Jordan cell structure, which is a reducible but indecomposable representation. 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. In this thesis, we briefly review conformal field theory and the appearance of logarithmic conformal field theories in the literature in the chronological order. Thereafter, we introduce the conventions and basic facts of logarithmic conformal field theory, and sketch an essential note on boundary conformal field theory. We have investigated cp,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 [22]. 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 [23, 24]. It is also presented how the differences between two constructions should be interpreted, resolved and extended beyond each case. Some discussions on possible applications are given in the final chapter.