Non Planar Topological 3-Vertex Formalism

Details Non Planar Topological 3-Vertex Formalism Non Planar Topological 3-Vertex Formalism

2007-12-27

arxiv.org/abs/0712.4249v2

Physics

High Energy Physics

High Energy Physics - Theory

43 pages, 12 figures, To appear in NPB

Scientific paper

Using embedding of complex curves in the complex projective plane $\bf{P }^{2}$, 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 | \longrightarrow \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.

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