Boundary states in a non rational asymmetric orbifold CFT

Two dimensional conformal field theory (CFT) provides the perturbative description of the worldsheet dynamics of string theory. For such a description, it is important to consider CFT correlation functions that, besides local operators, include line defects and boundaries preserving the conformal symmetry. In particular, worldsheets with boundaries correspond to strings in background of solitons, called D-branes. There are known methods to systematically study the consistent topological defects and boundary conditions in rational CFTs. The goal of this thesis is to study boundary states and topological defects in an example of a non-rational asymmetric orbifold CFT, where standard methods to get both of these objects are not applicable.