| Summary: | 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 τ , which is the large N duality of Chern-Simons theory for a framed unknot with integer framing τ 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 [56].
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