D1D5 System and Noncommutative Geometry

Supergravity on AdS3×S×T has dual description as a conformal sigma-model with the target space 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 noncommutative geometry. As a byproduct, we give a prediction on the dependence of the moduli space of instantons on the noncommutative T4 on the metric and the noncommutativity parameter. We give a compelling evidence that the moduli space of stringy instantons on R4 with the B field does not receive α′corrections. We also study the relation between the D1D5 sigma-model instantons and the supergravity instantons. On leave from the Institute of Theoretical and Experimental Physics, 117259, Bol. Cheremushkinskaya, 25, Moscow, Russia.