On matrix model compactification on non-commutative
                    <i>F</i>
                    <sub>0</sub>
                    geometry

Benkaddour, I.; Беннаи, М.; Diaf, E.; Saidi, El Hassan

doi:10.1088/0264-9381/17/8/303

Cited by 9 publications

(19 citation statements)

References 22 publications

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“…Moreover the solution of these eqs read, up to a normalization factor, as: 14) where x i are as in eqs(2.1), ̟ is the complex conjugate of ω and where 15) with α standing for ω k1 , ω k2 , ω k3 and their products. This solution shows clearly that Z 5 i , the product 4 i=1 Z i and their linear combination are all of them in the centre Z(Q nc ) of the NC algebra Q nc .…”

Section: Nc Quinticmentioning

confidence: 99%

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NC geometry and fractional branes

Saidi

2003

Class. Quantum Grav.

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Considering complex n-dimension Calabi-Yau homogeneous hyper-surfaces Hn with discrete torsion and using Berenstein and Leigh algebraic geometry method, we study Fractional D-branes that result from stringy resolution of singularities. We first develop the method introduced in hep-th/0105229 and then build the non commutative (NC) geometries for orbifolds O = Hn/Z n n+2 with a discrete torsion matrix t ab = exp[ i2π n+2 (η ab − η ba )], η ab ∈ SL(n, Z). We show that the NC manifolds O (nc) are given by the algebra of functions on the real (2n + 4) Fuzzy torus T 2(n+2)with q a i 's being charges of Z n n+2 . We also give graphic rules to represent O (nc) by quiver diagrams which become completely reducible at orbifold singularities. It is also shown that regular points in these NC geometries are represented by polygons with (n + 2) vertices linked by (n + 2) edges while singular ones are given by (n + 2) non connected loops. We study the various singular spaces of quintic orbifolds and analyze the varieties of fractional D branes at singularities as well as the spectrum of massless fields. Explicit solutions for the NC quintic Q (nc) are derived with details and general results for complex n dimension orbifolds with discrete torsion are presented.

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Section: Nc Quinticmentioning

confidence: 99%

“…taken to be proportional to the identity operator; that is g 1 g 2 g −1 1 g −1 2 = λ I id with λ ∈ C * as required by the Schur lemma [11,14].…”

Section: Nc Geometry and Discrete Torsionmentioning

confidence: 99%

NC geometry and fractional branes

Saidi

2003

Class. Quantum Grav.

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“…Moreover like for the U (1) r symmetry, the C * r toric group is abelian and the general properties of its representations are grosso-modo similar to those of U (1) r . In practice, the C * r toric group may be defined as given by the set of operators U a = λ Ta a , satisfying 13) and acting on the x i 's by the following gauge transformations,…”

Section: * R Toric Symmetrymentioning

confidence: 99%

“…These NC structures have found remarkable applications in various areas of quantum physics such as in the analysis of D(p−4)/Dp brane systems (p > 3) [6,7] and in the study of tachyon condensation using the GMS method [8]. However, most of NC spaces used in these studies involve mainly NC R d θ [9], NC T d θ torii [9,10], some cases of Z n type orbifolds of NC torii [11,12] and some generalizations to non commutative higher dimensional cycles such as the non commutative extension of Hizerbruch complex surfaces F n used in [13] and some special Calabi-Yau orbifolds.…”

Section: Introductionmentioning

confidence: 99%

Toric varieties with NC toric actions: NC type IIA geometry

Беннаи¹,

Saidi²

2004

Nuclear Physics B

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Extending the usual C * r actions of toric manifolds by allowing asymmetries between the various C * factors, we build a class of non commutative (NC) toric varieties V of the polygons associated to V d+1 . Moreover, we study fractional D branes at singularities and show that, due to the complete reducibility property of C * r group representations, there is an infinite number of fractional D branes. We also give the generalized Berenstein and Leigh quiver diagrams for discrete and continuous C * r representation spectrums.An illustrating example is presented.

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“…Note that for n = 1, the homogeneity group of R 4 is SU(2)× SP(1)∼ SO (4). In this case, F (ij) [αβ] = Ω αβ F (ij) and so eq (2.7) becomes…”

Section: Harmonic Analyticitymentioning

confidence: 99%

Explicit derivation of Yang-Mills self-dual solutions on non-commutative harmonic space

Belhaj¹,

Hssaini²,

Sahraoui³

et al. 2001

Class. Quantum Grav.

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We develop the noncommutative harmonic space (NHS) analysis to study the problem of solving the non-linear constraints eqs of noncommutative Yang-Mills selfduality in four-dimensions. We show that this space, denoted also as NHS(η, θ), has two SU(2) isovector deformations η (ij) and θ (ij) parametrising respectively two noncommutative harmonic subspaces NHS(η,0) and NHS(0,θ) used to study the selfdual and anti self-dual noncommutative Yang-Mills solutions. We reformulate the Yang-Mills self-dual constraint eqs on NHS(η,0) by extending the idea of harmonic analyticity to linearize them. Then we give a perturbative self dual solution recovering the ordinary one. Finally we present the explicit computation of an exact self-dual solution.

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On matrix model compactification on non-commutative F ₀ geometry

Cited by 9 publications

References 22 publications

NC geometry and fractional branes

NC geometry and fractional branes

Toric varieties with NC toric actions: NC type IIA geometry

Explicit derivation of Yang-Mills self-dual solutions on non-commutative harmonic space

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On matrix model compactification on non-commutative F 0 geometry

Cited by 9 publications

References 22 publications

NC geometry and fractional branes

NC geometry and fractional branes

Toric varieties with NC toric actions: NC type IIA geometry

Explicit derivation of Yang-Mills self-dual solutions on non-commutative harmonic space

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On matrix model compactification on non-commutative F ₀ geometry