Related papers: The Configuration space integral for links in R^3
We analyze the hamiltonian quantization of Chern-Simons theory associated to the universal covering of the Lorentz group SO(3,1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological…
The based loop space of a configuration space of points in a Euclidean space can be viewed as a space of pure braids in a Euclidean space of one dimension higher. We continue our study of such spaces in terms of Kontsevich's CDGA of…
We study the integrability from the spectral form factor in the Chern-Simons formulation. The effective action in the higher spin sector was not derived so far. Therefore, we begin from the SL(3) Chern-Simons higher spin theory. Then the…
We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds S by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of…
We study knots in 3d Chern-Simons theory with complex gauge group $SL(N,\mathbb{C})$, in the context of its relation with 3d $\mathcal{N}=2$ theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4…
Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. This paper is the first in a series where we…
A new set of projection operators for three-dimensional models are constructed. Using these operators, an uncomplicated and easily handling algorithm for analysing the unitarity of the aforementioned systems is built up. Interestingly…
This paper characterizes which subsets of C^n can be the set of positions of n points on a linkage in the complex plane C. For example, assuming compactness they are just compact semialgebraic sets. Noncompact configuration spaces are…
The functional integral computation of the various topological invariants, which are associated with the Chern-Simons field theory, is considered. The standard perturbative setting in quantum field theory is rewieved and new developments in…
A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six…
We show that the approaches to integrable systems via 4d Chern-Simons theory and via symmetry reductions of the anti-self-dual Yang-Mills equations are closely related, at least classically. Following a suggestion of Kevin Costello, we…
We identify a large class R of three-dimensional N=2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally…
Using the framework of White Noise Analysis we give a rigorous implementation of the gauge fixed Chern-Simons path integral associated to an arbitrary simple simply-connected compact structure group G and a simple class of (ribbon) links in…
We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Noether currents and superpotentials are computed…
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…
These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly $\su$. We give detailed examples, develop the…
There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is…
There is a higher dimensional analogue of the perturbative Chern-Simons theory in the sense that a similar perturbative series as in 3-dimension, which is computed via configuration space integral, yields an invariant of higher dimensional…
The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin…
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection,…