Noncommutative geometry from strings and branes

Ardalan, F.; Arfaei, H.; Sheikh-Jabbari, M. M.

doi:10.1088/1126-6708/1999/02/016

Cited by 291 publications

(343 citation statements)

References 23 publications

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“…A similar result is also obtained in [13,24] by considering the quantization of open strings ending on D-branes. The noncommutativity of string coordinates already appeared in earlier works [26,27].…”

Section: D-instantons On T 2 and T 2 θsupporting

confidence: 84%

“…There m is interpreted as the winding number of the resulting D-string. The same interpretation is also made in [4,13,14,18,20] and seems natural for the following reason, for example. Setting θ = B 12 = 0 in (4.17) yields 2πkn = (2π s ) 2 m, (4.19) which is consistent with the physical picture that each D-instanton has 'cell' of area 2πk because of the world volume noncommutativity (4.1) and the D-string wrapped m times over T 2 consists of n such cells.…”

Section: D-instantons On T 2 With the 2-form Field Fluxmentioning

confidence: 55%

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World volume noncommutativity versus target space noncommutativity

Kato¹,

Kuroki²

1999

J. High Energy Phys.

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It is known that the noncommutativity of D-brane coordinate is responsible for describing the higher-dimensional D-branes in terms of more fundamental ones such as D-particles or D-instantons, while considering a noncommutative torus as a target space is conjectured to be equivalent to introducing the background antisymmetric tensor field in matrix models. In the present paper we clarify the dual nature of both descriptions. Namely the noncommutativity of conjugate momenta of the D-brane coordinates realizes the target space structure, whereas noncommutativity of the coordinates themselves realizes world volume structure. We explicitly construct a boundary state for the Dirichlet boundary condition where the string boundary is adhered to the D-brane on the noncommutative torus. There are non-trivial relations between the parameters appeared in the algebra of the coordinates and that of the momenta.

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Section: D-instantons On T 2 and T 2 θsupporting

confidence: 84%

Section: D-instantons On T 2 With the 2-form Field Fluxmentioning

confidence: 55%

World volume noncommutativity versus target space noncommutativity

Kato¹,

Kuroki²

1999

J. High Energy Phys.

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“…It was suggested [8,9,10,11] that the noncommutative geometry can be reproduced in the elementary framework of constrained systems as a result of the Hamiltonian quantization of the system (2), (3), by analogy with the noncommutativity arising for coordinates of a charged particle in the lowest Landau level [13,14,15]. To achieve this, there were proposed rather radical modifications [8,11] of the Dirac procedure for constrained systems. There is some discrepancy among the results obtained in different approaches, which was discussed in [8,9,10,11,12,16,17].…”

Section: Introductionmentioning

confidence: 99%

“…To achieve this, there were proposed rather radical modifications [8,11] of the Dirac procedure for constrained systems. There is some discrepancy among the results obtained in different approaches, which was discussed in [8,9,10,11,12,16,17]. Let us talk about these issues for a while in order to put our work in a perspective.…”

Section: Introductionmentioning

confidence: 99%

Open string with a backgroundBfield as the first order mechanics, noncommutativity, and soldering formalism

et al. 2007

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To study noncommutativity properties of the open string with constant B-field we construct a mechanical action which reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit B −→ ∞. In particular, it is true for zero mode of the string coordinate which means that the noncommutativity is intrinsic property of this mechanical system. We describe the arbitrariness in the relation existent between the mechanical and the string variables and show that noncommutativity of the string variables on the boundary can be removed. It is in correspondence with the result of Seiberg and Witten on relation among noncommutative and ordinary Yang-Mills theories. The recently developed soldering formalism helps us to establish a connection between the original open string action and the Polyakov action.

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“…Among others, it has been found out that when D-branes accompany this system the worldvolume of the D-branes becomes noncommutative [4][5] [6] [7] [8].…”

Section: Introductionmentioning

confidence: 99%

p−p′ system with B field and projection operator noncommutative solitons

Murakami

2001

J. High Energy Phys.

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We study the system of the Dp -brane with Dp-brane (p < p ) inside, in the case where B ij field is a nonvanishing constant. In order to understand how the Dp-brane is viewed from the Dp -brane worldvolume theory, we investigate the process in which the Dp-brane is probed with p -p open string. We calculate the scattering amplitudes among p-p open strings and p -p open strings and show that not only the Weyl transform of the projection operator onto the ground state but also those onto higher excited states emerge as multiplicative factors of the amplitudes. *

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Noncommutative geometry from strings and branes

Cited by 291 publications

References 23 publications

World volume noncommutativity versus target space noncommutativity

World volume noncommutativity versus target space noncommutativity

Open string with a backgroundBfield as the first order mechanics, noncommutativity, and soldering formalism

p−p′ system with B field and projection operator noncommutative solitons

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