Related papers: Topological quantum field theory and hyperk\"ahler…
Rozansky and Witten proposed in 1996 a family of new three-dimensional topological quantum field theories, indexed by compact (or asymptotically flat) hyperkaehler manifolds. As a byproduct they proved that hyperkaehler manifolds also give…
A straightforward relationship between the two approaches to 3-dimensional topological invariants, one of them put forward by Witten in the framework of topological quantum field theory, and the second one proposed by Kohno in terms of…
Motivated by the similarity between CSW theory and the Chern Simons state for General Relativity in the Ashtekar variables, we explore what the universe would look like if it were in a state corresponding to a 3D TQFT. We end up with a…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We give an overview of 3-dimensional topological quantum field theories (TQFTs) and the corresponding quantum invariants of 3-manifolds. We…
We study Quot schemes of vector bundles on algebraic curves. Marian and Oprea gave a description of a topological quantum field theory (TQFT) studied by Witten in terms of intersection numbers on Quot schemes of trivial bundles. Since these…
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent…
We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary,…
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce some basic notions of Topological Quantum…
In this article, we discuss a (2+1)-dimensional topological quantum field theory, for short TQFT, with a Verlinde basis. As a conclusion of this general theory, we have a Dehn surgery formula. We show that Turaev-Viro-Ocneanu TQFT has a…
We discuss topological quantum field theories that compute topological invariants which depend on additional structures (or decorations) on three-manifolds. The $q$-series invariant $\hat{Z}(q)$ proposed by Gukov, Pei, Putrov and Vafa is an…
In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic…
In this paper, we establish the general theory of (2+1)-dimensional topological quantum field theory (in short, TQFT) with a Verlinde basis. It is a consequence that we have a Dehn surgery formula for 3-manifold invariants for this kind of…
A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields…
We formulate a deformation of Rozansky-Witten theory analogous to the $\Omega$-deformation. It is applicable when the target space $X$ is hyperk\"ahler and the spacetime is of the form $\mathbb{R} \times \Sigma$, with $\Sigma$ being a…
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…
We first construct the Rozansky-Witten model coupled to BF theory and Chern-Simons theory using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) method. Then we apply the machinery developed in some earlier papers about AKSZ theories and…
Topological quantum field theory (TQFT) is a powerful tool to describe homologies, which normally involve complexes and a variety of maps/morphisms, what makes a functional integration approach with a sum over a single kind of maps…
The paper has two parts, in the first part, we apply the localisation technique to the Rozansky-Witten theory on compact HyperK\"ahler targets. We do so via first reformulating the theory as some supersymmetric sigma-model. We obtain the…
A weight system on graph homology was constructed by Rozansky and Witten using a compact hyperk\"ahler manifold. A variation of this construction utilizing holomorphic vector bundles over the manifold gives a weight system on chord…
We construct extended TQFTs associated to Rozansky--Witten models with target manifolds $T^*\mathbb{C}^n$. The starting point of the construction is the 3-category whose objects are such Rozansky--Witten models, and whose morphisms are…