D1D5 system and noncommutative geometry

Supergravity on AdS(3) x S-3 x T-4 has a dual description as a conformal si gma-model with the target space being the moduli space of instantons on the noncommutative torus. We derive the precise relation between the parameter s of this noncommutative torus and the parameters of the near-horizon geome try. We show that the low energy dynamics of the system of D1D5-branes wrap ped 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 mo duli space of instantons on the noncommutative T-4 on the metric and the no ncommutativity parameter. We give a compelling evidence that the moduli spa ce of stringy instantons on R-4 with the B-field does not receive alpha'-co rrections. We also study the relation between the D1D5 sigma-model instanto ns and the supergravity instantons, (C) 2000 Elsevier Science B.V. All righ ts reserved.