7 research outputs found
Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups
We study the entanglement for a state on linked torus boundaries in
Chern-Simons theory with a generic gauge group and present the asymptotic
bounds of R\'enyi entropy at two different limits: (i) large Chern-Simons
coupling , and (ii) large rank of the gauge group. These results show
that the R\'enyi entropies cannot diverge faster than and ,
respectively. We focus on torus links with topological linking number
. The R\'enyi entropy for these links shows a periodic structure in and
vanishes whenever , where the integer
is a function of coupling and rank . We highlight that the
refined Chern-Simons link invariants can remove such a periodic structure in
.Comment: 31 pages, 5 figure
Eigenvalue hypothesis for multi-strand braids
Computing polynomial form of the colored HOMFLY-PT for non-arborescent knots
obtained from three or more strand braids is still an open problem. One of the
efficient methods suggested for the three-strand braids relies on the
eigenvalue hypothesis which uses the Yang-Baxter equation to express the answer
through the eigenvalues of the -matrix. In this paper, we generalize
the hypothesis to higher number of strands in the braid where commuting
relations of non-neighbouring matrices are also incorporated. By
solving these equations, we determine the explicit form for
-matrices and the inclusive Racah matrices in terms of braiding
eigenvalues (for matrices of size up to 6 by 6). For comparison, we briefly
discuss the highest weight method for four-strand braids carrying fundamental
and symmetric rank two representation. Specifically, we present all
the inclusive Racah matrices for representation and compare with the
matrices obtained from eigenvalue hypothesis.Comment: 23 page