Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-10-17
J.Phys. A38 (2005) 721-748
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, Latex
Scientific paper
10.1088/0305-4470/38/3/010
Using the algebraic geometric approach of Berenstein et {\it al} (hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with discrete torsion. We first develop a new way of getting complex $d$ mirror Calabi-Yau hypersurfaces $H_{\Delta}^{\ast d}$ in toric manifolds $M_{\Delta }^{\ast (d+1)}$ with a $C^{\ast r}$ action and analyze the general group of the discrete isometries of $H_{\Delta}^{\ast d}$. Then we build a general class of $d$ complex dimension NC mirror Calabi-Yau orbifolds where the non commutativity parameters $\theta_{\mu \nu}$ are solved in terms of discrete torsion and toric geometry data of $M_{\Delta}^{(d+1)}$ in which the original Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the NC algebra for generic $d$ dimensions NC Calabi-Yau manifolds and give various representations depending on different choices of the Calabi-Yau toric geometry data. We also study fractional D-branes at orbifold points. We refine and extend the result for NC $% (T^{2}\times T^{2}\times T^{2})/(\mathbf{{Z_{2}}\times {Z_{2})}}$ to higher dimensional torii orbifolds in terms of Clifford algebra.
Belhaj Adil
Saidi El Hassan
No associations
LandOfFree
NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-671799