TY - JOUR

T1 - Non-commutative Calabi - Yau manifolds

AU - Berenstein, David

AU - Leigh, Robert G.

N1 - Funding Information:
We wish to thank M. Ando and V. Jejjala for discussions. Work supported in part by US Department of Energy, grant DE-FG02-91ER40677 and an Outstanding Junior Investigator Award.

PY - 2001/2/1

Y1 - 2001/2/1

N2 - We discuss aspects of the algebraic geometry of compact non-commutative Calabi - Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi - Yau algebra. We consider two examples: A toroidal orbifold T6/Z2 x Z2, and an orbifold of the quintic in CP4, each with discrete torsion. The non-Commutative geometry tools are enough to describe various properties of the orbifolds. First, one describes correctly the fractionation of branes at singularities. Secondly, for the first example we show that one can recover explicitly a large slice of the moduli space of complex structures which deform the orbifold. For this example we also show that we get the correct counting of complex structure deformations at the orbifold point by using traces of non-commutative differential forms (cyclic homology).

AB - We discuss aspects of the algebraic geometry of compact non-commutative Calabi - Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi - Yau algebra. We consider two examples: A toroidal orbifold T6/Z2 x Z2, and an orbifold of the quintic in CP4, each with discrete torsion. The non-Commutative geometry tools are enough to describe various properties of the orbifolds. First, one describes correctly the fractionation of branes at singularities. Secondly, for the first example we show that one can recover explicitly a large slice of the moduli space of complex structures which deform the orbifold. For this example we also show that we get the correct counting of complex structure deformations at the orbifold point by using traces of non-commutative differential forms (cyclic homology).

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U2 - 10.1016/S0370-2693(01)00005-3

DO - 10.1016/S0370-2693(01)00005-3

M3 - Article

AN - SCOPUS:0000094658

SN - 0370-2693

VL - 499

SP - 207

EP - 214

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1-2

ER -