On Non Commutative Calabi-Yau Hypersurfaces

Abstract

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.

16 pages, Latex. One more subsection on fractional branes, one reference and minor changes are added. To appear in Phy. Let.B

References in corpus (7)

• Solitons in Noncommutative Gauge Theory
• Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
• Resolution of Stringy Singularities by Non-commutative Algebras
• Tachyon Condensation on Noncommutative Torus
• Non-Commutative Calabi-Yau Manifolds
• On HyperKahler Singularities
• Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space

Cited by in corpus (8)

• Theta functions on Noncommutative T^4
• N-Point Deformation of Algebraic K3 Surfaces
• Toric Varieties with NC Toric Actions: NC Type IIA Geometry
• On Non-Commutative Orbifolds of K3 Surfaces
• On Non Commutative G2 structure
• NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
• A Matrix Model for ν_{k_1k_2}=\frac{k_1+k_2}{k_1 k_2} Fractional Quantum Hall States
• Non-commutative ADE geometries as holomorphic wave equations