Related papers: On three-dimensional topological field theories co…
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…
We investigate the Chung-Fukuma-Shapere theory, or Kuperberg theory, of three-dimensional lattice topological field theory. We construct a functor which satisfies the Atiyah's axioms of topological quantum field theory by reformulating the…
We study the relation between lattice construction and surgery construction of three-dimensional topological field theories. We show that a class of the Chung-Fukuma-Shapere theory on the lattice has representation theoretic reformulation…
In this article we analyze a two dimensional lattice gauge theory based on a quantum group.The algebra generated by gauge fields is the lattice algebra introduced recently by A.Yu.Alekseev,H.Grosse and V.Schomerus we define and study wilson…
In this work, we employ the Tannaka-Krein reconstruction to compute the quantum double $\mathcal D(\mathcal G)$ of a finite 2-group $\mathcal G$ as a Hopf monoidal category. We also construct a 3+1D lattice model from the Dijkgraaf-Witten…
We construct and classify topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, we impose invariance under arbitrary topology-preserving deformations of the underlying…
We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that are not distinguishable by observables. We…
A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a…
Motivated by the question of exploring the "theory space" of quantum field theories, we review the concept of "decomposing" and "gluing" quantum field theories. We explain this in the context of three-dimensional $\mathcal{N}=2$…
We consider a two parameter family of $Z_2$ gauge theories on a lattice discretization $T(M)$ of a 3-manifold $M$ and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space…
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…
In this paper we look at 3D lattice models that are generalizations of the state sum model used to define the Kuperberg invariant of 3-manifolds. The partition function is a scalar constructed as a tensor network where the building blocks…
Motivated by some previously known facts from mathematical and physics literature, we explore certain relations between 3-dimensional topological gauge theories with continuous and finite gauge groups, commonly known as Chern-Simons (CS)…
The goal of this paper is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately…
We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semi-simple Hopf algebras. A character…
We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate…
Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the…
We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus $g$, the partition function $Z$ is defined for a triangulation consisting of $n$ triangles of…
We extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…
We introduce a technique to construct gapped lattice models using defects in topological field theory. We illustrate with 2+1 dimensional models, for example Chern-Simons theories. These models are local, though the state space is not…