相关论文: Combinatorial Formulae for Vassiliev Invariants fr…

Recently proposed new gauge invariant formulation of the Chern-Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore it is found that the canonical (Noether) Poincar\'e…

Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects…

We study three-dimensional Chern-Simons theory with complex gauge group SL(2,C), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single…

Some years ago, it was conjectured by the first author that the Chern-Simons perturbation theory of a 3-manifold at the trivial flat connection is a resurgent power series. We describe completely the resurgent structure of the above series…

Invariant polynomials for torus links are obtained in the framework of the Chern-Simons topological gauge theory. The polynomials are computed as vacuum expectation values on the three-sphere of Wilson line operators representing the…

This work applies the ideas of Alekseev and Meinrenken's Non-commutative Chern-Weil Theory to describe a completely combinatorial and constructive proof of the Wheeling Theorem. In this theory, the crux of the proof is, essentially, the…

The universal Vassiliev-Kontsevich invariant is a functor from the category of tangles to a certain graded category of chord diagrams, compatible with the Vassiliev filtration and whose associated graded is an isomorphism. The Vassiliev…

We show that the perturbative part of the partition function in the Chern-Simons theory on a 3-sphere as well as the central charge and expectation value of the unknotted Wilson loop in the adjoint representation can be expressed in terms…

A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and…

We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex…

The Vassiliev-Gusarov link invariants of finite type are known to be closely related to perturbation theory for Chern-Simons theory. In order to clarify the perturbative nature of such link invariants, we introduce an algebra V_infinity…

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these…

It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we…

Invariants for framed links in $S^3$ obtained from Chern-Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct a three-manifold invariant. This is a generalization of a similar construction…

We generalize several results on Chern-Simons models on Sigma x S1 in the so-called "torus gauge" which were obtained in arXiv:math-ph/0507040 to the case of general (simply-connected simple compact) structure groups and general link…

We use the Chern-Simons quantum field theory in order to prove a recently conjectured limitation on the 1/K expansion of the Jones polynomial of a knot and its relation to the Alexander polynomial. This limitation allows us to derive a…

The occurrence of the Askey-Wilson (AW) algebra in the $SU(2)$ Chern-Simons (CS) theory and in the Reshetikhin-Turaev (RT) link invariant construction with quantum algebra $U_q(\mathfrak{su}_2)$ is explored. Tangle diagrams with three…

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…

The colored Jones function of a knot is a sequence of Laurent polynomials that encodes the Jones polynomial of a knot and its parallels. It has been understood in terms of representations of quantum groups and Witten gave an intrinsic…

We give a generalization of the Reshetikhin-Turaev functor for tangles to get a combinatorial formula for the universal Vassiliev-Kontsevich invariant of framed oriented links which is coincident with the Kontsevich integral. The universal…