Defect Lines, Dualities, and Generalised Orbifolds in Quantum Field Theory
This paper explores the intricate role defects play in promoting our understanding of quantum field theories (QFT), with a particular emphasis on two-dimensional conformal field theories (CFT). The authors explore the conceptual framework where defect lines and their junction points serve as pivotal elements in describing symmetries, dualities, and orbifold constructions.
Defects in Quantum Field Theory
The utilization of defects as `inhomogeneities' naturally arises in the analysis of QFTs and statistical mechanics. Defects can manifest as discontinuities along hypersurfaces, bearing direct implications on the expectation values within a theory. The paper discusses well-known duality symmetries, such as electric-magnetic duality and Kramers-Wannier duality, illustrating how defects facilitate the mapping between these dual descriptions.
A significant aspect explored is the analysis of one-dimensional defects (defect lines) in two-dimensional CFT. These not only describe universality classes of defect lines in lattice models but also aid in probing the intrinsic symmetries and structures within CFTs. The composition and fusion of defect operators are fundamental tools used to interpret order-disorder dualities and construct orbifold models.
Symmetries and Order-Disorder Dualities
In the paper, the authors identify certain defects as conformal or topological based on their interaction with the stress tensor. Of particular interest are topological defects, which possess properties allowing deformation on the world sheet without altering correlation functions. The fusion algebra of these defects is dissected, revealing how it corresponds to the symmetry and duality structures of the underlying CFT.
The paper elucidates the role of defect junctions in characterizing order-disorder dualities, providing insights through explicit examples such as the Ising model. The authors show that topological defect operators adhere to fusion rules consistent with the model's symmetry group, leading to the revelation of inherent duality transformations enabled by the defects.
Orbifolds and Generalization
A key contribution of this paper is the generalization of the orbifold construction through the lens of defect nets. Traditionally, orbifolds involve symmetry operations facilitated by group-like defects. Here, the authors broaden this perspective by emphasizing a generalized approach that accommodates more complex topological defects.
The core methodology involves assembling defect networks capable of retaining topological invariance across transformations depicted by moves like Matveev iterations. The intricate structure of these defect networks and their junctions captures the essence of generalized orbifold constructions and paves the way for a unified framework that encompasses various rational CFTs known for exceptional modular invariants.
Implications and Future Directions
This exploration yields substantial theoretical and practical implications. The paper presents a versatile toolset that can significantly enrich our handling of defects in QFT and CFT, potentially leading to new physical predictions. By extending the orbifold concept through a robust mathematical framework, it opens novel avenues for constructing and interpreting complex CFTs beyond conventional limits.
Future developments might explore applying these findings to advanced topics like non-rational CFTs or further unifying different classes of defects. As a result, this work not only enhances our comprehension of inherent symmetries and dualities but also serves as a foundation for subsequent breakthroughs in theoretical physics.