D1D5 System and Noncommutative Geometry

Abstract

Supergravity on $Ad{S}_3\times S^3\times {\mathbf{T}}^4$ has a dual description as a conformal sigma-model with the target space being the moduli space of instantons on the noncommutative torus. We derive the precise relation between the parameters of this noncommutative torus and the parameters of the near-horizon geometry. We show that the low energy dynamics of the system of $D1D5$ branes wrapped on the torus of finite size is described in terms of the noncommutative geometry. As a byproduct, we give a prediction on the dependence of the moduli space of instantons on the noncommutative ${\mathbf{T}}^4$ on the metric and the noncommutativity parameter. We give a compelling evidence that the moduli space of stringy instantons on ${\mathbf{R}}^4$ with the $B$ field does not receive ${\alpha }^{\prime }$-corrections. We also study the relation between the $D1D5$ sigma-model instantons and the supergravity instantons.

latex, 45 pp., 2 figures, references and explanations added

References in corpus (3)

• String Theory and Noncommutative Geometry
• D-branes and Deformation Quantization
• More Comments on String Theory on AdS_3

Cited by in corpus (13)

• Microscopic Formulation of Black Holes in String Theory
• Permeable conformal walls and holography
• Trieste lectures on solitons in noncommutative gauge theories
• The chiral ring of AdS3/CFT2 and the attractor mechanism
• Phase Structure of Non-Commutative Field Theories and Spinning Brane Bound States
• Dp-D(p+4) in Noncommutative Yang-Mills
• Instantons and Emergent AdS_3 x S^3 Geometry
• Constructions of Non Commutative Instantons on $T^4$ and $K_3$
• Emergent AdS3 and BTZ Black Hole from Weakly Interacting Hot 2d CFT
• Tachyon condensation and `bounce' in the D1-D5 system
• D1/D5 system and Wilson Loops in (Non-)commutative Gauge Theories
• Rolling tachyon in anti-de Sitter space-time
• Duality and Combinatorics of Long Strings in ADS3