Vassiliev Invariants for Links from Chern-Simons Perturbation Theory
arXiv:hep-th/9607030 · doi:10.1016/S0550-3213(96)00689-X
Abstract
The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel the algebraic structure encoded in the group factors of the perturbative series expansion. In the process a factorization theorem is proved for Wilson lines. Wilson lines are then closed back into Wilson loops and new link invariants of finite type are defined. Integral expressions for these invariants are presented for the first three primitive ones of lower degree in the case of two-component links. In addition, explicit numerical results are obtained for all two-component links of no more than six crossings up to degree four.
44 pages, LaTex, epsf.sty, 15 figures
References in corpus (4)
- Vassiliev knot invariants and Chern-Simons perturbation theory to all orders
- Numerical knot invariants of finite type from Chern-Simons perturbation theory
- A Relation Between the Kauffman and the HOMFLY Polynomials for Torus Knots
- Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity
Cited by in corpus (16)
- Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
- Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix
- Colored HOMFLY polynomials for the pretzel knots and links
- Kontsevich Integral for Vassiliev Invariants from Chern-Simons Perturbation Theory in the Light-Cone Gauge
- Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux
- Towards effective topological field theory for knots
- On genus expansion of superpolynomials
- Racah matrices and hidden integrability in evolution of knots
- HOMFLY polynomials in representation [3,1] for 3-strand braids
- Quantum Racah matrices and 3-strand braids in irreps R with |R|=4
- Cabling procedure for the colored HOMFLY polynomials
- Combinatorial Formulae for Vassiliev Invariants from Chern-Simons Gauge Theory
- Vassiliev invariants: a new framework for quantum gravity
- Gauge-Invariant Operators for Singular Knots in Chern-Simons Gauge Theory
- Embedded graph invariants in Chern-Simons theory
- Vassiliev Invariants for Flows Via Chern-Simons Perturbation Theory