Knot Invariants for Intersecting Loops

Details Knot Invariants for Intersecting Loops Knot Invariants for Intersecting Loops

1992-12-22

arxiv.org/abs/hep-th/9212137v1

Phys.Lett. B305 (1993) 214-222

Physics

High Energy Physics

High Energy Physics - Theory

22 pages

Scientific paper

10.1016/0370-2693(93)90110-4

We generalize the braid algebra to the case of loops with intersections. We introduce the Reidemeister moves for 4 and 6-valent vertices to have a theory of rigid vertex equivalence. By considering representations of the extended braid algebra, we derive skein relations for link polynomials, which allow us to generalize any link Polynomial to the intersecting case. We perturbatively show that the HOMFLY Polynomials for intersecting links correspond to the vacuum expectation value of the Wilson line operator of the Chern Simon's Theory. We make contact with quantum gravity by showing that these polynomials are simply related with some solutions of the complete set of constraints with cosmological constant

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