Related papers: A cellular topological field theory
We study the perturbative quantization of 2-dimensional massive scalar field theory with polynomial (or power series) potential on manifolds with boundary. We prove that it fits into the functorial quantum field theory framework of…
In this work we discuss the construction of "simplicial BF theory", the field theory with finite-dimensional space of fields, associated to a triangulated manifold, that is in a sense equivalent to topological BF theory on the manifold…
The off-shell nilpotent BRST charge and the BRST invariant effective action for non-abelian BF topological theories over D-dimensional manifolds are explicitly constructed. These theories have the feature of being reducible with exactly D-3…
This note studies the quantized corner structure of four-dimensional $BF$ theory, classifies the associated free and physical corner algebras and constructs possible representations. In the abelian case, for arbitrary closed oriented…
We give an introduction for the non-expert to TQFT (Topological Quantum Field Theory), focussing especially on its role in algebraic topology. We compare the Atiyah axioms for TQFT with the Eilenberg Steenrod axioms for homology, give a few…
Consistent interactions that can be added to a two-dimensional, free abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master…
In this paper, we construct a new topological quantum field theory of cohomological type and show that its partition function is a crossing number.
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 study anisotropic scaling limits of topological field theories using tropical geometry. The resulting topological field theories are characterized by foliated geometries and are invariant under foliation-preserving gauge transformations.…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
BF theory is a topological field theory that appears in different parts of theoretical physics and one of its important uses is in lower dimensional holography settings. While it can be defined as a dimensional reduction of 3D CS theory, it…
Cobordism categories have played an important role in classical geometry and more recently in mathematical treatments of quantum field theory. Here we will compute localisations of two-dimensional discrete cobordism categories. This allows…
$BF$ theories defined over non trivial line bundles are studied. It is shown that such theories describe a realization of a non trivial higher order bundle. The partition function differs from the usual one -in terms of the Ray Singer…
We consider a deformation of the BF theory in any dimension by means of the antifield BRST formalism. Possible consistent interaction terms for the action and the gauge symmetries are analyzed and we find a new class of topological gauge…
We discuss the structure of auxiliary fields for non-Abelian BF theories in arbitrary dimensions. By modifying the classical BRST operator, we build the on-shell invariant complete quantum action. Therefore, we introduce the auxiliary…
We consider a deformation of three dimensional BF theory by means of the antifield BRST formalism. Possible deformations for the action and the gauge symmetries are analyzed. We find a new class of gauge theories which include nonabelian BF…
For a cellular algebra $\A$ with a cellular basis $\ZC$, we consider a decomposition of the unit element $1_\A$ into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular…
We show how the framework of crossed simplicial groups may be used to provide a classification of topological field theories on open cobordism categories defined by reductions of the structure group to a planar Lie group. Such theories are…
Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions…
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…