Non Planar Topological 3-Vertex Formalism

Abstract

Using embedding of complex curves in the complex projective plane ${\mathbf{P}}^2$, we develop a \emph{non planar} topological 3-vertex formalism for topological strings on the family of local Calabi-Yau threefolds $X^{(m,-m,0)}=\mathcal{O}(m)\oplus \mathcal{O}(-m)\to E^{(t,\infty )}$. The base $E^{(t,\infty )}$ stands for the degenerate elliptic curve with Kahler parameter $t$; but a large complex structure $\mu$; i.e $|\mu |⟶\infty$. We also give first results regarding A-model topological string amplitudes on $X^{(m,-m,0)}$. The 2D $U(1)$ gauged $\mathcal{N}=2$ supersymmetric sigma models of the degenerate elliptic curve $E^{(t,\infty )}$ as well as for the family $X^{(m,-m,0)}$ are studied and the role of D- and F-terms is explicitly exhibited.

43 pages, 12 figures, To appear in NPB

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Cited by in corpus (5)

• Entropy of Pairs of Dual Attractors in 6D/7D
• BPS and non BPS 7D Black Attractors in M-Theory on K3
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Refining the Shifted Topological Vertex
• Quiver Gauge Models in F-Theory on Local Tetrahedron