Noncommutative geometry and Matrix theory

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.

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

confidence: 64%

Section: Compactification On Noncommutative Two-torusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

World volume noncommutativity versus target space noncommutativity

Kato¹,

Kuroki²

1999

“…The recent interest in noncommutative geometry and its appearance in string theory [1][2][3], has been limited almost exclusively to the case where the noncommutative coordinates are spacelike:…”

Section: Introductionmentioning

confidence: 99%

Strings in background electric field, space/time noncommutativity and a new noncritical string theory

Seiberg

Susskind

Toumbas

2000

269

494

Searching for space/time noncommutativity we reconsider open strings in a constant background electric field. The main difference between this situation and its magnetic counterpart is that here there is a critical electric field beyond which the theory does not make sense. We show that this critical field prevents us from finding a limit in which the theory becomes a field theory on a noncommutative spacetime. However, an appropriate limit toward the critical field leads to a novel noncritical string theory on a noncommutative spacetime. 5/00

“…Recently there has been a revival of interest in field theories on noncommutative spaces [1] [2], especially those that emerge as various limits of M theory compactifications [3]. The latest circumstances in which such theories were found involve D-branes in the presence of a background Neveu-Schwarz B-field [4] [5].…”

Section: Introductionmentioning

confidence: 99%

Monopoles and strings in noncommutative gauge theory

Gross¹,

Nekrasov²

2000

138

189

We study some non-perturbative aspects of noncommutative gauge theories. We find analytic solutions of the equations of motion, for noncommutative U(1) gauge theory, that describe magnetic monopoles with a finite tension string attached. These solutions are non-singular, finite and sourceless. We identify the string with the projection of a D-string ending on a D3-brane in the presence of a constant B-field. 05/00