Related papers: Unoriented topological quantum field theory and li…
Turaev and Turner introduced a bijection between unoriented topological quantum field theories and extended Frobenius algebras. In this paper, we will show that there exists a bijective correspondence between unoriented (1 + 1)-dimensional…
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
The structure of topological quantum field theories on the compact Kahler manifold is interpreted. The BRST transformations of fields are derived from universal bundle and the observables are found from the second Chern class of universal…
We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…
This thesis presents a thorough analysis of the links between the N=4 supersymmetric gauge theory in four dimensions and its three topological twisted counterparts. Special emphasis is put in deriving explicit results in terms of the vacuum…
In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate…
We propose a quantum field theory description of the X-cube model of fracton topological order. The field theory is not (and cannot be) a topological quantum field theory (TQFT), since unlike the X-cube model, TQFTs are invariant (i.e.…
We discuss unifying features of topological field theories in 2, 3 and 4 dimensions. This includes relations among enumerative geometry (2d topological field theory) link invariants (3d Chern-Simons theory) and Donaldson invariants (4d…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces.…
A homology and cohomology theory for topological quandles are introduced. The relation between these (co)homology groups and quandle (co)homology groups are studied. The 1 - topological quandle cocycles are used to compute state sum…
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R^d the new theory differs from the original one by the spectrum of operators. Sometimes the local…
Description of two three-dimensional topological quantum field theories of Witten type as twisted supersymmetric theories is presented. Low-energy effective action and a corresponding topological invariant of three-dimensional manifolds are…
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots…
We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not necessarily even. For every plane diagram of…