Compactification of M(atrix) theory on noncommutative toroidal orbifolds

Anatoly Konechny; Albert Schwarz

doi:10.1016/S0550-3213(00)00544-7

Compactification of M(atrix) theory on noncommutative toroidal orbifolds

Anatoly Konechny, Albert Schwarz

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Abstract

It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori arise naturally in consideration of toroidal compactifications of M(atrix) theory. A similar analysis of toroidal Z₂ orbifolds leads to the algebra B_θthat can be defined as a crossed product of noncommutative torus and the group Z₂. Our paper is devoted to the study of projective modules over B_θ(Z₂-equivariant projective modules over a noncommutative torus). We analyze the Morita equivalence (duality) for B_θalgebras working out the two-dimensional case in detail.

Original language	English
Pages (from-to)	667-684
Number of pages	8
Journal	Nuclear Physics B
Volume	591
Issue number	3
DOIs	https://doi.org/10.1016/S0550-3213(00)00544-7
Publication status	Published - 25 Dec 2000

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title = "Compactification of M(atrix) theory on noncommutative toroidal orbifolds",

abstract = "It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori arise naturally in consideration of toroidal compactifications of M(atrix) theory. A similar analysis of toroidal Z2 orbifolds leads to the algebra Bθ that can be defined as a crossed product of noncommutative torus and the group Z2. Our paper is devoted to the study of projective modules over Bθ (Z2-equivariant projective modules over a noncommutative torus). We analyze the Morita equivalence (duality) for Bθ algebras working out the two-dimensional case in detail.",

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AU - Schwarz, Albert

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N2 - It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori arise naturally in consideration of toroidal compactifications of M(atrix) theory. A similar analysis of toroidal Z2 orbifolds leads to the algebra Bθ that can be defined as a crossed product of noncommutative torus and the group Z2. Our paper is devoted to the study of projective modules over Bθ (Z2-equivariant projective modules over a noncommutative torus). We analyze the Morita equivalence (duality) for Bθ algebras working out the two-dimensional case in detail.

AB - It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori arise naturally in consideration of toroidal compactifications of M(atrix) theory. A similar analysis of toroidal Z2 orbifolds leads to the algebra Bθ that can be defined as a crossed product of noncommutative torus and the group Z2. Our paper is devoted to the study of projective modules over Bθ (Z2-equivariant projective modules over a noncommutative torus). We analyze the Morita equivalence (duality) for Bθ algebras working out the two-dimensional case in detail.

U2 - 10.1016/S0550-3213(00)00544-7

DO - 10.1016/S0550-3213(00)00544-7

M3 - Article

SN - 0550-3213

VL - 591

SP - 667

EP - 684

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -

Compactification of M(atrix) theory on noncommutative toroidal orbifolds

Abstract

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