相关论文: Non-invertible symmetries and boundaries in four d…
We explore topological defects in the 4-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb{Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality…
Non-invertible Kramers-Wannier (KW) duality symmetries are constructed for the transverse-field Ising model (TFIM) at the self-dual point under various boundary conditions (BCs), as long as the resultant Hamiltonian commutes with the ${\rm…
We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes…
In recent years we have learned that several four-dimensional field theories can manifest non-invertible zero-form symmetries generalizing the Kramers-Wannier duality defect of the 2d critical Ising model. Several recent works by various…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to…
We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models in $2$ dimensions, with electromagnetic duality for finite gauge theories in $3$ dimensions. The…
This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a…
We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the $\mathbb{Z}_2$-orbifold of the…
The Kramers-Wannier duality introduces a well-known non-invertible symmetry in the critical transverse-field Ising model. In this work, we extend this concept to a broad class of quantum lattice models induced from integrability, providing…
Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain…
The algebraic approach to quantum field theory focuses on the properties of local algebras, whereas the study of (possibly non-invertible) global symmetries emphasizes global aspects of the theory and spacetime. We study connections between…
Kramers-Wannier dualities in lattice models are intimately connected with symmetries. We show that they can be found directly and explicitly from the symmetry transformations of the boundary states in the underlying conformal field theory.…
We revisit electric and magnetic surface charges and edge modes in four-dimensional Maxwell theory and QED on a spacetime with a finite spatial boundary. Using the S-wall, which implements electromagnetic duality, we clarify the dual…
We study how non-invertible self-duality defects arise in theories with a holographic dual. We focus on the paradigmatic example of $\mathfrak{su}(N)$ $\mathcal{N} = 4$ SYM. The theory is known to have non-invertible duality and triality…
For a class of two-dimensional Euclidean lattice field theories admitting topological lines encoded into a spherical fusion category, we explore aspects of their realisations as boundary theories of a three-dimensional topological quantum…
Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and…
What does it mean for a boundary condition to be symmetric with respect to a non-invertible global symmetry? We discuss two possible definitions in 1+1d. On the one hand, we call a boundary weakly symmetric if the symmetry defects can…
We study different aspects of integrable boundary quantum field theories, focusing mostly on the ``boundary sine-Gordon model'' and its applications to condensed matter physics. The first part of the review deals with formal problems. We…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…