Related papers: Fusion Rules for $\mathbb{Z}/2\mathbb{Z}$ Permutat…
We find the fusion rules for the quantum analogues of the complex reflection groups $H_n^s=\mathbb Z_s\wr S_n$. The irreducible representations can be indexed by the elements of the free monoid $\mathbb N^{*s}$, and their tensor products…
We study non-invertible duality symmetries by gauging a diagonal subgroup of a non-anomalous U(1) $\times$ U(1) global symmetry. In particular, we employ the half-space gauging to $c=2$ bosonic torus conformal field theory (CFT) in two…
We construct a class of non-invertible duality defects, in (2+1)d quantum field theories, arising from half-spacetime gauging of a 2-group symmetry. Starting from a parent theory with two discrete and Abelian 0-form symmetries and a…
The fusion rules of the 2-permutation orbifold of an arbitrary lattice vertex operator algebra are determined by using the theory of quantum dimension.
The fusion rules in $\mathrm{Rep}_f D(G)$ for a finite group $G$ can be computed in terms of character inner products. Using an explicit formula for these fusion rules, we show that $\mathrm{Rep}_f D(G)$ is multiplicity free for two…
The initial classification of fusion rules have shown that rational conformal field theory is very limited. In this paper we study the fusion rules of extend ed current algebras. Explicit formulas are given for the S matrix and the fusion…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…
We investigate quantum corrections in non-commutative gauge theory on fuzzy sphere. We study translation invariant models which classically favor a single fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the two…
A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative…
We consider the derived category of permutation modules over a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the set underlying the tt-spectrum of compact…
The fusion products of admissible representations of the su(2) WZW model at the fractional level k=-4/3 are analysed. It is found that some fusion products define representations for which the spectrum of L_0 is not bounded from below.…
"Fusion rules" are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras, in turn, are…
A closed formula for the structure constants in the SL(2,C)/SU(2) WZNW model is derived by a method previously used in Liouville theory. With the help of a reflection amplitude that follows from the structure constants one obtains a…
In topological phases of matter, fusion rules dictate how anyonic topological charges combine. However, the transformation of quasiparticle mobility under fusion remains largely unexplored. In this letter, we reveal that restricted mobility…
This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime…
We study the noncommutative base change of an entwining structure $(A,C,\psi)$ by a Grothendieck category $\mathfrak S$, using two module like categories. These are the categories of entwined comodule objects and entwined contramodule…
We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive…
N-fold tensor products of a rational CFT carry an action of the permutation group S_N. These automorphisms can be used as gluing conditions in the study of boundary conditions for tensor product theories. We present an ansatz for such…
We study the IR behavior of noncommutative gauge theory in the matrix formulation. We find that in this approach, the nature of the UV/IR mixing is easily understood, which allows us to perform a reliable calculation of the quantum…
For any finite group G with a finite G-set X and a modular tensor category C we construct a part of the algebraic structure of an associated G-equivariant monoidal category: For any group element g in G we exhibit the module category…