Related papers: Categorical Continuous Symmetry
We propose that the symmetry category associated to a 2D quantum field theory with 0-form $G$-symmetry with 't Hooft anomaly $k\in H^4(BG,\mathbb{Z})$ for a large class of Lie groups $G$ is the category of twisted measurable fields of…
Ocneanu's tube algebra provides a finite algorithm to compute the Drinfeld center of a fusion category. In this work we reveal the universal property underlying the tube algebra. Take a base category $\mathcal V$ which is strongly concrete,…
We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the…
We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category…
We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe 't Hooft anomalies and classify gapped phases stabilized by these symmetries,…
For a zero-temperature Landau symmetry breaking transition in $n$-dimensional space that completely breaks a finite symmetry $G$, the critical point at the transition has the symmetry $G$. In this paper, we show that the critical point also…
Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest…
We investigate the most general gauging operations in 2+1 dimensional oriented field theories with finite symmetry groups, which correspond to gapped boundary conditions in 3+1 dimensional Dijkgraaf-Witten theory. The classification is…
We investigate symmetry topological field theories (SymTFTs) of non-abelian and non-invertible symmetries and the different Lagrangian algebras associated with a given Drinfeld center. For several examples we analyze the condensable…
Symmetry is a powerful tool for studying dynamics in QFT: it provides selection rules, constrains RG flows, and often simplifies analysis. Currently, our understanding is that the most general form of symmetry is described by categorical…
We study one-dimensional disordered systems with average non-invertible symmetries, where quenched disorder may locally break part of the symmetry while preserving it upon disorder averaging. A canonical example is the random…
We use the Symmetry Topological Field Theory (SymTFT) to study and classify gapped phases in (2+1)d for a class of categorical symmetries, referred to as being of bosonic type. The SymTFTs for these symmetries are given by twisted and…
This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological…
We propose a framework for fusion category symmetry on the (1+1)D lattice in the infinite-volume limit by giving a formal interpretation of SymTFT decompositions. Our approach is based on axiomatizing physical boundary subalgebra of…
Matching 't Hooft anomalies is a powerful tool for constraining the low-energy dynamics of quantum systems and their allowed renormalization group (RG) flows. For non-invertible (or categorical) symmetries, however, a key challenge has been…
We discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented…
In this paper we develop a graded tilting theory for gauged Landau-Ginzburg models of regular sections in vector bundles over projective varieties. Our main theoretical result describes - under certain conditions - the bounded derived…
We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a…
We introduce, for a symmetric fusion category $\mathcal{A}$ with Drinfeld centre $\mathcal{Z}(\mathcal{A})$, the notion of $\mathcal{Z}(\mathcal{A})$-crossed braided tensor category. These are categories that are enriched over…
We present a new model for continuous tensor categories as algebra objects in the Morita bicategory of $\mathrm{C}^*$-algebras. In this setting, we generalize the construction of Tambara-Yamagami tensor categories from finite abelian groups…