Refined topological strings on local ℙ 2

Abstract

We calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on ℙ 2 (the local ℙ 2). The refined topological vertex formalism can not be directly applied to local ℙ 2 therefore we use the properties of the refined Hopf link to define a new two legged vertex which together with the refined vertex gives the partition function of the local ℙ 2.