D1D5 System and Noncommutative Geometry

TL;DR

This paper explores the duality between supergravity on a specific AdS space and a conformal sigma-model on a noncommutative torus, revealing how noncommutative geometry influences the moduli space of instantons and the dynamics of D1D5 branes.

Contribution

It establishes a precise relation between noncommutative torus parameters and near-horizon geometry, and predicts how instanton moduli spaces depend on noncommutativity and metric parameters.

Findings

Derived the relation between noncommutative torus parameters and supergravity geometry.

Predicted the dependence of instanton moduli space on noncommutativity and metric.

Provided evidence that stringy instanton moduli spaces do not receive '-corrections.

Abstract

Supergravity on $AdS_3\times S^3\times {\bf T}^4$ 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 ${\bf T}^4$ on the metric and the noncommutativity parameter. We give a compelling evidence that the moduli space of stringy instantons on ${\bf R}^4$ with the $B$ field does not receive $\alpha'$-corrections. We also study the relation between the $D1D5$ sigma-model instantons and the supergravity instantons.