arXiv subjects

Houda Jehjouh

Publications and source records attributed to Houda Jehjouh.

4 recordsLinked to original sources

arXiv2008

Topological String on Toric CY3s in Large Complex Structure Limit

We develop a non planar topological vertex formalism and we use it to study the A-model partition function $\mathcal{Z}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that purpose, we first consider the $T^{2}\times R$ special Lagrangian fibration of generic CY3-folds and we give the realization of the class of large $μ$ toric CY3-folds in terms of supersymmetric gauged linear sigma model with \emph{non zero} gauge invariant superpotentials $% \mathcal{W}(Φ) $. Then, we focus on a one complex parameter supersymmetric $U(1) $ gauged model involving six chiral superfields ${Φ_{i}}$ with $\mathcal{W}=μ(\prod\nolimits_{i=0}^{5}Φ_{i}) $ and we use it to compute the function $\mathcal{Z}_{top}$ for the case of the local elliptic curve in the limit $μ\to \infty $.

hep-th↗

arXiv2008

Refining the Shifted Topological Vertex

We study aspects of the refining and shifting properties of the 3d MacMahon function $\mathcal{C}_{3}(q) $ used in topological string theory and BKP hierarchy. We derive the explicit expressions of the shifted topological vertex $\mathcal{S}_{λμν}(q) $ and its refined version $\mathcal{T}_{λμν}(q,t) $. These vertices complete results in literature.

hep-th↗

arXiv2008

Non Planar Topological 3-Vertex Formalism

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 $μ$; i.e $| μ| \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.

hep-th↗

arXiv2008

Generalized MacMahon G(q) as q-deformed CFT Correlation Function

Using $Γ_{\pm}(z) $ vertex operators of the $c=1$ two dimensional conformal field theory, we give a 2d-quantum field theoretical derivation of the conjectured d- dimensional MacMahon function G$_{d}(q) $. We interpret this function G$_{d}(q) $ as a $(d+1) $- point correlation function $\mathcal{G}_{d+1}(z_{0},...,z_{d}) $ of some local vertex operators $\mathcal{O}%_{j}(z_{j}) $. We determine these operators and show that they are particular composites of q-deformed hierarchical vertex operators $% Γ_{\pm}^{(p)}$, with a positive integer p. In agreement with literature's results, we find that G$_{d}(q) $, $d\geq 4$, cannot be the generating functional of all \textit{d- dimensional} generalized Young diagrams .

hep-th↗