On explicit formulae of LMOV invariants

TL;DR

This paper derives explicit formulas for LMOV invariants associated with the resolved conifold with an Aganagic-Vafa brane, advancing understanding of open string invariants in toric Calabi-Yau 3-folds.

Contribution

It provides explicit formulae for LMOV invariants in the resolved conifold with an AV-brane for any integer framing, extending previous theoretical results.

Findings

Explicit formulas for LMOV invariants derived

Verification of integrality properties in prior work

Application of string dualities to compute invariants

Abstract

We started a program to study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane) several years ago. This paper is devoted to the case of resolved conifold with one out AV-brane in any integer framing $\tau$, which is the large $N$ duality of Chern-Simons theory for a framed unknot with integer framing $\tau$ in $S^3$. By using the methods from string dualities, we compute several explicit formulae of the corresponding LMOV invariants for this special model, whose integrality properties have been proved in a separated paper.