### Matrix Compactification On Orientifolds

, 1998

"... Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space Rd /Γ as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry gr ..."

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Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space Rd /Γ as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry group Γ on Euclidean space Rd and a projective representation U of Γ. The choice of Hilbert space on which the algebra of U is realized as an operator algebra corresponds to the choice of a physical background for the compactification. All these data are summarized The original Matrix model [1] was formulated as a microscopic model for the M theory in eleven dimensional spacetime. To describe the real world one needs to understand how to compactify the theory to lower dimensions. In the absence of a rank-three antisymmetric tensor field background, the description of the compactification of Matrix

### Double Compactified D=11 Supermembrane Dual as a Non-Commutative Super-Maxwell Theory

, 2000

"... The physical hamiltonian of the double compactified D = 11 supermembrane dual with non trivial wrapping is explicitly obtained. It contains cubic and quartic interacting terms. It exactly agrees with the hamiltonian formulation of non-commutative super-Maxwell theory on the world volume, minimally c ..."

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The physical hamiltonian of the double compactified D = 11 supermembrane dual with non trivial wrapping is explicitly obtained. It contains cubic and quartic interacting terms. It exactly agrees with the hamiltonian formulation of non-commutative super-Maxwell theory on the world volume, minimally coupled to seven scalars fields corresponding to the transverse coordinates to the brane. The non commutative star product is intrinsically obtained from the simplectic 2-form defined by the minimal configuration of the hamiltonian, that is by the pull-back to the world volume of the canonical conection 1-form on the Hopf fibring over CPn. The constraint generating the area preserving diffeomorphism is reformulated as the Gauss constraint of the non-commutative super-Maxwell theory.

### NEIP-98-022 hep-th/9812219 Noncommutative Open String and D-brane

, 1999

"... In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that spacetime coordinates of the open string end-points become noncommutative, and correspondingly the D-brane worldvolume also becomes noncommutative. This provides a string theory deri ..."

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In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that spacetime coordinates of the open string end-points become noncommutative, and correspondingly the D-brane worldvolume also becomes noncommutative. This provides a string theory derivation and generalization of the noncommutativity obtained previously in the M(atrix) model compactification. For Dp-branes with p ≥ 2 our results are new and agree with that of M(atrix) theory for the case of M(atrix) theory [1] compactified on a torus is described by a supersymmetric Yang-Mills (SYM) theory living on the dual torus [1, 2]. However, this simple picture no longer holds when a background field is present. It was shown by Connes, Douglas and Schwarz in [3] that for the M(atrix) model compactified on a T 2, noncommutative SYM arises

### IPM/P-98/22 hep-th/9810179 Super Yang-Mills Theory on Noncommutative Torus from Open Strings Interactions

, 1998

"... Institute for studies in theoretical Physics and Mathematics IPM, ..."

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### IPM/P-98/19 hep-th/9810072 Noncommutative Geometry from Strings and Branes F. Ardalana,b, H. Arfaeia,b a 1

, 1999

"... Noncommutative torus compactification of Matrix model is shown to be a direct consequence of quantization of the open strings attached to a D-membrane with a nonvanishing background B field. We calculate the BPS spectrum of such a brane system using both string theory results and DBI action. The DBI ..."

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Noncommutative torus compactification of Matrix model is shown to be a direct consequence of quantization of the open strings attached to a D-membrane with a nonvanishing background B field. We calculate the BPS spectrum of such a brane system using both string theory results and DBI action. The DBI action leads to a new transformation property of the compactification radii under the SL(2,Z)N transformations. 1

### NEIP-98-022 hep-th/yymmddd Noncommutative Open String and D-brane

, 1998

"... In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that spacetime coordinates of the open string end-points become noncommutative, and correspondingly the D-brane worldvolume also becomes noncommutative. This provides a string theory deri ..."

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In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that spacetime coordinates of the open string end-points become noncommutative, and correspondingly the D-brane worldvolume also becomes noncommutative. This provides a string theory derivation and generalization of the noncommutativity obtained previously in the Matrix model compactification. For Dp-branes with p> 2 our results are new and they are different from a naive generalization of the M(atrix) theory [1] compactified on a torus is described by a supersymmetric Yang-Mills (SYM) theory living on the dual torus [1, 2]. However, this simple picture no longer holds when a background field is present. It was shown by Connes, Douglas and Schwarz in [3] that for the M(atrix) model compactified on a T 2, noncommutative SYM arises

### IPM/P-99/04 hep-th/9901080 Open Strings in a B-field Background as Electric

, 1999

"... Institute for studies in theoretical Physics and Mathematics IPM, ..."

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