Related papers: A quick guide to defect orbifolds
When a quantum field theory in $d$-spacetime dimensions possesses a global $(d-1)$-form symmetry, it can decompose into disjoint unions of other theories. This is reflected in the physical quantities of the theory and can be used to study…
In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint…
We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically…
In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical…
We revisit the possibility of constructing non-invertible topological defects for the axial symmetry of massless QED, despite its ABJ anomaly. Dressing the defects with a topological quantum field theory with mixed $U(1)$ and…
We propose defect lines as a useful tool to study bulk perturbations of conformal field theories, in particular to analyse the induced renormalisation group flows of boundary conditions. As a concrete example we investigate bulk…
In this work we study particular TQFTs in three dimensions, known as Symmetry Topological Field Theories (or SymTFTs), to identify line defects of two-dimensional CFTs arising from the compactification of 6d $(2,0)$ SCFTs on 4-manifolds…
In recent work N. Hitchin introduced the concept of "generalised geometry". The key feature of generalised structures is that that they can be acted on by both diffeomorphisms and 2-forms, the so-called $B$-fields. In this lecture, we give…
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
We investigate the global structure of topological defects which wrap a submanifold $F\subset M$ in a quantum field theory defined on a closed manifold $M$. The Pontryagin-Thom construction oversees the interplay between the global…
Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to…
This note is intended as an introduction to the functorial formulation of quantum field theories with defects. After some remarks about models in general dimension, we restrict ourselves to two dimensions - the lowest dimension in which…
We develop a general theory of 3-dimensional ``orbifold completion'', to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. Given a semistrict 3-category $\mathcal{T}$ with adjoints for all…
In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S…
Given any symmetry acting on a $d$-dimensional quantum field theory, there is an associated $(d+1)$-dimensional topological field theory known as the Symmetry TFT (SymTFT). The SymTFT is useful for decoupling the universal quantities of…
A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of…
The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…
It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a…
We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…