Chern-Simons Theory, Colored-Oriented Braids and Link invariants

Abstract

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 correlators of $SU(2{)}_k$ Wess-Zumino conformal field theory are presented. A large class of representations of the generators of the groupoid of coloured-oriented braids are obtained. These provide a whole lot of new link invariants of which Jones polynomials are the simplest examples. These new invariants are explicitly calculated as illustrations for knots upto eight crossings and two-component multicoloured links upto seven crossings.

48 pages + 20 diagrams

References in corpus (2)

• Three Dimensional Chern-Simons Theory as a Theory of Knots and Links
• Complete Solution of SU(2) Chern-Simons Theory

Cited by in corpus (29)

• Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
• Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid
• Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
• Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants
• Kontsevich Integral for Vassiliev Invariants from Chern-Simons Perturbation Theory in the Light-Cone Gauge
• Entanglement Entropy and the Colored Jones Polynomial
• Colored Kauffman Homology and Super-A-polynomials
• SU(N) quantum Racah coefficients & non-torus links
• Cabling procedure for the colored HOMFLY polynomials
• Entropy of Quantum Black Holes
• Quantum geometry and quantum algorithms
• Chern-Simons Theory, Knot Invariants, Vertex Models and Three-manifold Invariants
• Knots, links, and long-range magic
• On R-matrix approaches to knot invariants
• Quantum Knitting
• Three-Manifold Invariants from Chern-Simons Field Theory with Arbitrary Semi-Simple Gauge Groups
• Combinatorial Formulae for Vassiliev Invariants from Chern-Simons Gauge Theory
• The representations of Temperley-Lieb-Jones algebras
• Quantum Computation of Jones' Polynomials
• Quantum automata, braid group and link polynomials
• Computation of Lickorish's Three Manifold Invariants using Chern-Simons Theory
• Gauge-Invariant Operators for Singular Knots in Chern-Simons Gauge Theory
• Musings on SVD and pseudo entanglement entropies
• Complexity for link complement States in Chern Simons Theory
• Spin networks, quantum automata and link invariants
• Three-partite vertex model and knot invariants
• On knots, complements, and 6j-symbols
• Bi-partite vertex model and multi-colored link invariants
• Level-rank duality of knot and link invariants