Related papers: Refined Chern-Simons Theory in Genus Two
We analyze the 2+1 dimensional gauge theory with two fermions in the real adjoint representation with non-zero Chern-Simons level. We propose a new fermion-fermion dualities between strongly-coupled theories and determine the quantum phase…
We study representations of the mapping class group of the punctured torus on the double of a finite dimensional possibly non-semisimple Hopf algebra that arise in the construction of universal, extended topological field theories. We…
The amplitudes of refined Chern-Simons (CS) theory, colored by antisymmetric (or symmetric) representations, conjecturally generate the Lambda^r- (or S^r-) colored triply graded homology of (n,m) torus knots. This paper is devoted to the…
In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds…
Chern-Simons theories, which are topological quantum field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of quantum field theories which can be exactly and…
We introduce the notion of $n$-dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension $n$. The familiar closed or open-closed TQFTs are special cases of…
We study the cohomology of $G$-representation varieties and $G$-character stacks by means of a topological quantum field theory (TQFT). This TQFT is constructed as the composite of a so-called field theory and the 6-functor formalism of…
We show that a vector space valued TQFT constructed in work of De Renzi et al. [DGGPR23] extends naturally to a topological field theory which takes values in the symmetric monoidal category of linear cochains. Specifically, we consider a…
Recent studies in several interrelated areas -- from combinatorics and representation theory in mathematics to quantum field theory and topological string theory in physics -- have independently revealed that many classical objects in these…
We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the $(0,1,2)$-dimensional part of…
Starting from an abelian group $G$ and a factorizable ribbon Hopf $G$-bialgebra $H$, we construct a TQFT $J_H$ for connected framed cobordisms between connected surfaces with connected boundary decorated with cohomology classes with…
We study the six-dimensional (2,0) superconformal field theory on S^1 x S^2 x M via compactification to five dimensions, where M is a three-manifold. Twisted along M, the five-dimensional theory has a half of N = (2,2) supersymmetry on S^2,…
A TQFT is a functor from a cobordism category to the category of vector spaces, satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant 2+1-cobordism…
We give a fresh introduction to the Khovanov Homology theory for knots and links, with special emphasis on its extension to tangles, cobordisms and 2-knots. By staying within a world of topological pictures a little longer than in other…
We review a construction of a new class of algebraic curves, called super-A-polynomials, and their quantum generalizations. The super-A-polynomial is a two-parameter deformation of the A-polynomial known from knot theory or Chern-Simons…
This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module…
We present a general framework for TQFT and related constructions using the language of monoidal categories. We construct a topological category C and an algebraic category D, both monoidal, and a TQFT functor is then defined as a certain…
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for…
In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over $n$-bit vectors taking $m$-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT)…
Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of…