SO(N) Reformulated Link Invariants from Topological Strings

TL;DR

This paper extends the reformulation of link invariants from U(N) to SO(N) Chern-Simons theory using topological string theory, revealing new polynomial invariants with integer coefficients and exploring their topological significance.

Contribution

It introduces a novel reformulation of SO(N) link invariants via topological strings, paralleling U(N) results, and investigates their topological meaning.

Findings

SO(N) link invariants can be expressed as polynomials with integer coefficients.

The reformulated invariants have a similar structure to U(N) invariants.

The topological interpretation of these invariants relates to orientifold dualities.

Abstract

Large N duality conjecture between U(N) Chern-Simons gauge theory on $S^3$ and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the conjectured form for the expectation value of the topological operators in A-model string theory led to a reformulation of link invariants in U(N) Chern-Simons theory giving new polynomial invariants whose integer coefficients could be given a topological meaning. We show that the A-model topological operator involving SO(N) holonomy leads to a reformulation of link invariants in SO(N) Chern-Simons theory. Surprisingly, the SO(N) reformulated invariants also has a similar form with integer coefficients. The topological meaning of the integer coefficients needs to be explored from the duality conjecture relating SO(N) Chern-Simons theory to A-model closed string theory on orientifold of the resolved conifold background.