Related papers: Twisted Drinfeld Centers and Framed String-Nets
We detail a construction of a symmetric monoidal structure, called the reduced tensor product on the 2-category of braided tensor categories $\mathbf{BTC}(\mathcal{A})$ containing a fixed symmetric fusion subcategory $\mathcal{A}$. The…
The present work shows that magnetic quivers encode the necessary information for determining the Drinfeld center in the symmetry topological field theory constructions (SymTFT) associated to a given absolute theory. The crucial argument…
We consider the tube algebra of a spherical semisimple multitensor category $\mathcal{X}$, and construct a braided monoidal structure with twist for its representations. We further show that this category is braided tensor equivalent with…
New classes of distance-constrained structures are introduced, namely string-node nets and meshes, a mesh being a string-node net for which the nodes are dense in the strings. Various construction schemes are given including the minimal…
Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…
Complex structures are determined for surfaces with $S^2$ and $T^2$ topologies generated by the dynamical triangulation method. For a surface with $S^2$ topology the spacial distribution of the conformal mode is obtained, while for the case…
I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.
We define a symmetric tensor product on the Drinfeld centre of a symmetric fusion category, in addition to its usual tensor product. We examine what this tensor product looks like under Tannaka duality, identifying the symmetric fusion…
With applications in mind to the representations and cohomology of block algebras, we examine elements of the graded center of a triangulated category when the category has a Serre functor. These are natural transformations from the…
In this work, inspired by some physical intuitions, we define a series of symmetry enriched categories to describe symmetry enriched topological (SET) orders, and define a new tensor product, called the relative tensor product, which…
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
In this paper we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups. Our methods depend on the theory of braided strict monoidal categories which are…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras,…
We construct tensor and bitensor categories with given Grothedieck rig (fusion algebra) in simple cases. The results provide examples on which to test the conjectural construction of 4-D TQFT's proposed by Crane and Frenkel and shed light…
Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data - S, T and fusion matrices - are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain…
We study an analogue of the Drinfel'd double for algebroids associated with the $O(D,D+n)$ gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three…
We define the twisted tensor product of two enriched categories, which generalizes various sorts of `products' of algebraic structures, including the bicrossed product of groups, the twisted tensor product of (co)algebras and the double…
We describe Lagrangian algebras in twisted Drinfeld centres for finite groups. Using the full centre construction, we establish a 1-1 correspondence between Lagrangian algebras and module categories over pointed fusion categories.
In this thesis, we report on results in non-anticommutative field theory and twistor string theory, trying to be self-contained. We first review the construction of non-anticommutative N=4 super Yang-Mills theory and discuss a…