Related papers: Chern-Simons Theory and the $R$-Matrix
The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable…
The superspace geometry of Chern-Simons forms is shown to be closely related to that of the 3-form multiplet. This observation allows to simplify considerably the geometric structure of supersymmetric Chern-Simons forms and their coupling…
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also…
Our recent paper~\cite{FST} with Claudia Scheimbauer uses the cobordism hypothesis to construct fully local Chern-Simons theories. Here we expose some physics motivations: Yang-Mills plus Chern-Simons in the bosonic case and the free…
An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this…
We consider the geometric quantisation of Chern--Simons theory for closed genus-one surfaces and semisimple complex groups. First we introduce the natural complexified analogue of the Hitchin connection in K\"{a}hler quantisation, with…
We propose a new partially topological theory in three dimensions which couples Chern-Simons theory to matter. The 3-manifolds needed for this construction admit transverse holomorphic foliation (THF). The theory depends only on the choice…
A general formula for physical observables in Chern-Simons theory with an arbitrary compact Lie group $G$, on an arbitrary closed oriented three-dimensional manifold $\cM$ is derived in terms of vacuum expectation values of Wilson loops in…
This is the 10th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It reviews correspondences between three-dimensional gauge theories and complex Chern-Simons theory on suitable…
In this paper, we generalize the arithmetic Chern-Simons theory to regular flat separated schemes of finite type over rings of integers of number fields by applying the duality theorems for arithmetic schemes.
The purpose of this article is to study the correspondence between $3d$-gravity and the Chern-Simons field theory from the perspective of geometric mechanics, specifically in the case where the structure group is the general affine group.…
A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In…
The partition function of complex Chern-Simons theory on a 3-manifold with torus boundary reduces to a finite dimensional state-integral which is a holomorphic function of a complexified Planck's constant $\tau$ in the complex cut plane and…
In this work we study the analogues of R-matrices that arise in 5d non-commutative topological-holomorphic Chern-Simons theory, which is known to describe twisted M-theory. We first study the intersections of line and surface operators in…
A correspondence between three-dimensional flat connections and constant curvature four-dimensional simplices is used to give a novel quantization of geometry via complex SL(2,C) Chern-Simons theory. The resulting quantum geometrical states…
We present a formal but simple calculational scheme to relate the expectation value of Wilson loops in Chern-Simons theory to the Jones polynomial. We consider the exponential of the generator of homotopy transformations which produces the…
We give an a priori construction of the two-dimensional reduction of three-dimensional quantum Chern-Simons theory. This reduction is a two-dimensional topological quantum field theory and so determines to a Frobenius ring, which here is…
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…
The canonical structure of higher dimensional pure Chern-Simons theories is analysed. It is shown that these theories have generically a non-vanishing number of local degrees of freedom, even though they are obtained by means of a…
The maximal extension of supersymmetric Chern-Simons theory coupled to fundamental matter has $\mathcal{N} = 3$ supersymmetry. In this short note, we provide the explicit form of the action for the mass-deformed $\mathcal{N} = 3$…