Related papers: Chern-Simons Theory on a General Seifert 3-Manifol…
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…
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…
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…
The topological non-Abelian Chern-Simons theory with a boundary is shown to require a scalar field companion in order to preserve overall gauge-invariance both in the 3 dimensional manifold, as well as on its boundary. This scalar field,…
A new, formal, non-combinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of non-perturbative topological quantum Chern-Simons theory, corresponding to an arbitrary compact…
The invariant integration method for Chern-Simons theory defined on the compact hyperbolic manifold {\Gamma}\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function is presented. We discuss…
We present an elementary review of some aspects of Chern-Simons theory with complex gauge group SL(N,C). We discuss some of the challenges in defining the theory as a full-fledged TQFT, as well as some successes inspired by the 3d-3d…
The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of…
Chern-Simons gauge theory is formulated on three dimensional $Z_2$ orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum…
A refined expression for the Faddeev-Popov determinant is derived for gauge theories quantised around a reducible classical solution. We apply this result to Chern-Simons perturbation theory on compact spacetime 3-manifolds with…
The 3d $A$-model is a two-dimensional approach to the computation of supersymmetric observables of three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. In principle, it allows us to compute half-BPS partition functions on any…
We formulate Poisson Chern-Simons gauge theories on compact group manifolds. These describe a sector of the large representation limit of noncommutative Chern-Simons in the same way as the light-cone formulation of the membrane action…
We study 5d N=2 maximally supersymmetric Yang-Mills theory with a gauge group G on S^2 x M_3, where M_3 is a 3-manifold. By explicit localization computation we show that the path-integral of the 5d N=2 theory reduces to that of the 3d G_C…
Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge…
We consider the Gopakumar-Ooguri-Vafa correspondence, relating ${\rm U}(N)$ Chern-Simons theory at large $N$ to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $\mathbb{S}^{\Gamma} =…
Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This…
In this paper, we show how to discretize the abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary 2D closed orientable manifolds. We find that, as long as a…
We formulate the Chern-Simons action for any compact Lie group using Deligne cohomology. This action is defined as a certain function on the space of smooth maps from the underlying 3-manifold to the classifying space for principal bundles.…
We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to this…
A generalization of the 4d Chern-Simons theory action introduced by Costello and Yamazaki is presented. We apply general arguments from symplectic geometry concerning the Hamiltonian action of a symmetry group on the space of gauge…