Related papers: Simple-current algebra constructions of 2+1D topol…
A discrete non-linear $\sigma$-model is obtained by triangulate both the space-time $M^{d+1}$ and the target space $K$. If the path integral is given by the sum of all the complex homomorphisms $\phi: M^{d+1} \to K$, with an partition…
All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete…
We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant…
The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of…
We classify connected \'etale algebras $A$'s in multiplicity-free modular fusion categories (MFCs) $\mathcal{B}$'s at rank six, namely $\text{rank}(\mathcal{B})=6$. There are eight MFCs in total and the result indicates that only $so(5)_2$…
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…
Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary monoidal 2-category. Examples of rigid algebras include…
We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…
We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a…
We propose a generic construction of exactly soluble \emph{local bosonic models} that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a 3+1D $Z_2$ gauge…
The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…
We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by…
We present practical and formal methods for gauging non-invertible symmetries in (2+1)d topological quantum field theories. Along the way, we generalize various aspects of invertible 0-form gauging, including symmetry fractionalization,…
In this paper we consider 4d $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an…
The soft factorization theorem for 4D abelian gauge theory states that the $\mathcal{S}$-matrix factorizes into soft and hard parts, with the universal soft part containing all soft and collinear poles. Similarly, correlation functions on…
A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted $Z$-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins.…
The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained (in part) from momentum space. Recently, Real Space…
In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for $so(2p+1)_2$. These categories describe non-abelian anyons dubbed `metaplectic anyons'. We…
In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…
A Hamiltonian formulation of the classical world-sheet theory in a generic, geometric or non-geometric, NSNS background is proposed. The essence of this formulation is a deformed current algebra, which is solely characterised by the…