Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-08-20
Phys.Lett. B523 (2001) 191-198
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, Latex. One more subsection on fractional branes, one reference and minor changes are added. To appear in Phy. Let.B
Scientific paper
10.1016/S0370-2693(01)01317-X
Using the algebraic geometry method of Berenstein et al (hep-th/0005087), we reconsider the derivation of the non commutative quintic algebra ${\mathcal{A}}_{nc}(5)$ and derive new representations by choosing different sets of Calabi-Yau charges ${C_{i}^{a}}$. Next we extend these results to higher $d$ complex dimension non commutative Calabi-Yau hypersurface algebras ${\mathcal{A}}_{nc}(d+2)$. We derive and solve the set of constraint eqs carrying the non commutative structure in terms of Calabi-Yau charges and discrete torsion. Finally we construct the representations of ${\mathcal{A}}_{nc}(d+2) $ preserving manifestly the Calabi-Yau condition $ \sum_{i}C_{i}^{a}=0$ and give comments on the non commutative subalgebras.
Belhaj Adil
Saidi El Hassan
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