Topological and conformal interfaces in two-dimensional quantum field theories
| dc.contributor.advisor | Konechny, Associate Professor Anatoly | |
| dc.contributor.author | Vergioglou, Vasileios | |
| dc.date.accessioned | 2026-02-25T09:36:16Z | |
| dc.date.issued | 2025-09 | |
| dc.description | We study conformal boundary conditions, topological defects as well as various concepts related to their presence in two-dimensional Rational Conformal Field Theories (RCFTs). In this situation, one new concept for example is a topological defect line with one of its ends attached to a boundary. Such junctions are called open topological defects. The first goal of this thesis is to consider new fusing matrices that arise from the existence of such junctions in our theory. For instance, one type of fusing matrices is related to the fusion of two open defects while another arises when an open defect junction passes through a boundary operator. The former appears in the structure constants of an associative algebra known as the boundary tube algebra while the latter plays an important role in constraining boundary Renormalisation Group (RG) flows triggered by that boundary operator. We use the Topological Field Theory (TFT) approach to RCFTs based on Frobenius algebra objects in Modular Tensor Categories (MTCs) to describe the general structure associated with such matrices and how to compute them from a given MTC, Frobenius algebra object and its representation theory. We illustrate the computational process on the rational free boson theories where we also discuss applications to boundary RG flows. Our second goal, motivated by applications in RG flows, is to classify pairs consisting of a local operator and a topological defect which commutes or anticommutes with it. We discuss both bulk and boundary versions of the problem. In the case of the charge conjugation modular invariant (anti-)commuting configurations in each problem can be obtained when a certain condition on the fusion rules is realised. We study the corresponding fusion rule problems in detail. While in the bulk case it reduces to realising the a × b = c fusion rule which was studied in [1], in the boundary it leads to a new type of problem. We obtain a full solution to this problem for the SU(2) and SU(3) Wess–Zumino–Witten (WZW) models and minimal models. We present a way to obtain solutions in the case of general WZW models using simple currents. | |
| dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Award. | |
| dc.identifier.uri | https://www.ros.hw.ac.uk/handle/10399/5313 | |
| dc.language.iso | en | |
| dc.publisher | Mathematical and Computer Sciences | |
| dc.title | Topological and conformal interfaces in two-dimensional quantum field theories | |
| dc.type | Doctor of Philosophy |