Related papers: Symmetries from outer automorphisms and unorthodox…
We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees…
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1 \times M_3$ with a non-trivial holonomy of a discrete global symmetry along the $S^1$.…
Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…
We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure,…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
Quantum Field Theories engineered in M-theory can have 2-group symmetries, mixing 0-form and 1-form symmetry backgrounds in non-trivial ways. In this paper we develop methods for determining the 2-group structure from the boundary geometry…
Global Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries, held at the Perimeter Institute for…
The past decade has seen a remarkable resurgence of the old programme of finding more or less a priori axioms for the mathematical framework of quantum mechanics. The new impetus comes largely from quantum information theory; in contrast to…
It is well-known that the cohomology of symmetric quandles generates robust cocycle invariants for unoriented classical and surface links. Expanding on the recently introduced module-theoretic generalized cohomology for symmetric quandles,…
A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are…
We systematically obtain all linear models which propagate a totally symmetric rank-three field without parity violation on a flat background. Each such model is defined exclusively by its gauge symmetry, a necessary property of effective…
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…
Special conformal field theories can have symmetry groups which are interesting sporadic finite simple groups. Famous examples include the Monster symmetry group of a $c=24$ two-dimensional conformal field theory (CFT) constructed by…
An extended Hubbard model with phonons is considered on a D-dimensional lattice. The symmetries of the model are studied in various cases. It is shown that for a certain choice of the parameters a superconducting SU_q(2) holds as a true…
We show that the 't Hooft anomaly of a quantum field theory with continuous flavor symmetry can be detected from rearrangements of the topological defect webs implementing the global symmetry in general spacetime dimension, which is…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
Wigner's classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective unitary representations can be reduced to…
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…