BPS Invariants for a Knot in Seifert Manifolds

TL;DR

This paper computes homological blocks for knots in Seifert manifolds with SU(N) gauge group by analytically continuing the Chern-Simons level, providing new insights into knot invariants in these 3-manifolds.

Contribution

It introduces a method to derive homological blocks for knots in Seifert manifolds through analytic continuation of the Chern-Simons level and representation data.

Findings

Homological blocks for knots in Seifert manifolds are explicitly calculated.

The method involves analytic continuation of the Chern-Simons level.

Results apply to Seifert integer homology spheres.

Abstract

We calculate homological blocks for a knot in Seifert manifolds when the gauge group is $SU(N)$. We obtain the homological blocks with a given representation of the gauge group from the expectation value of the Wilson loop operator by analytically continuing the Chern-Simons level. We also obtain homological blocks with the analytically continued level and representation for a knot in the Seifert integer homology spheres.