Related papers: Microscopic Models for Fusion Categories
Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes…
We classify fusion categories which are Morita equivalent to even parts of subfactors with index $3+\sqrt{5} $, and module categories over these fusion categories. For the fusion category $\mathcal{C} $ which is the even part of the…
A recently-developed molecular field theory (MFT) has been used to fit single-crystal magnetic susceptibility chi versus temperature T data below the respective antiferromagnetic ordering temperatures TN for a variety of collinear and…
A near-group fusion category is a fusion category C where all but 1 simple objects are invertible. Examples of these include the Tambara-Yamagami categories and the even sectors of the E6 and affine-D5 subfactors, though there are…
We introduce the notion of double cosets relative to two fusion subcategories of a fusion category. Given a tensor functor $F : \C \to \D$ between fusion categories, we introduce an equivalence relation $\approx^F$ on the set $\Lambda_\C$…
We discuss universal properties of conformal field theories with holographic duals. A central feature of these theories is the existence of a low-lying sector of operators whose correlators factorize. We demonstrate that factorization can…
To connect conformal field theories (CFT) to probabilistic lattice models, recent works [HKV22, Ada23] have introduced a novel definition of local fields of the lattice models. Local fields in this picture are probabilistically concrete:…
Conformal Field Theories (CFTs) are special classes of quantum field theories that find applications ranging from critical phenomena to theories of quantum gravity via holography. Understanding thermal effects in CFTs is crucial:…
The flux quanta attachment to the electrons creates composite fermions (CFs). The mass, the size and the density of the CF are inconsistent with real material. The sequence of fractional charges which suggest formation of CF agrees with the…
A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler…
Any N=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral…
Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of…
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
This is the continuation of our study of the Levin-Wen model based on an arbitrary unitary fusion category $\mathcal{C}$ on the infinite plane. The ground state of the Levin-Wen model hosts anyonic excitations whose fusion and braiding…
We consider the triality fusion category discovered in the $c = 1$ KT theory \cite{Thorngren:2021yso}. We analyze this fusion category using the tools from the group theoretical fusion category and describe how to compute the simple lines,…
Our previously developed Constrained-Pairing Mean-Field Theory (CPMFT) is shown to map onto an Unrestricted Hartree-Fock (UHF) type method if one imposes a corresponding pair constraint to the correlation problem that forces occupation…
Automatic detection of abnormal cervical cells from Thinprep Cytologic Test (TCT) images is a critical component in the development of intelligent computer-aided diagnostic systems. However, existing algorithms typically fail to effectively…
Counterfactual explanations (CFEs) are minimal and semantically meaningful modifications of the input of a model that alter the model predictions. They highlight the decisive features the model relies on, providing contrastive…
We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional conformal field theory (CFT) associated…
Accurate tumor segmentation in PET/CT images is crucial for computer-aided cancer diagnosis and treatment. The primary challenge lies in effectively integrating the complementary information from PET and CT images. In clinical settings, the…