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NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration

Mohamed Bennai·El Hassan Saidi
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Abstract

Using the algebraic geometry method of Berenstein and Leigh (BL), hep-th/0009209 and hep-th/0105229), and considering singular toric varieties ${\cal V}_{d+1}$ with NC irrational torus fibration, we construct NC extensions ${\cal M}_{d}^{(nc)}$ of complex d dimension Calabi-Yau (CY) manifolds embedded in ${\cal V}_{d+1}^{(nc)}$. We give realizations of the NC $\mathbf{C}^{\ast r}$ toric group, derive the constraint eqs for NC Calabi-Yau (NCCY) manifolds ${\cal M}^{nc}_d$ embedded in ${\cal V}_{d+1}^{nc}$ and work out solutions for their generators. We study fractional $D$ branes at singularities and show that, due to the complete reducibility property of $\mathbf{C}^{\ast r}$ group representations, there is an infinite number of non compact fractional branes at fixed points of the NC toric group.

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Mohamed Bennai, El Hassan Saidi. 2002-10-08. NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration. https://doi.org/10.1016/s0370-2693(02)02962-3

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