Supergravity solutions for Dp-D(6 − p) bound states: from p = 7 to p = −1

Abstract

Near horizon geometries of Dp-branes with p ≠ 3 are singular with a running dilaton. Bound states of Dp branes with their magnetic cousins, D(6 − p) branes, can stabilise the dilaton such that an AdS factor might appear in the near horizon region, potentially leading to a chain of AdS vacua of the form AdS_p+2 × S^p+2 × 𝕋^6−2p. The solutions with p = −1, 1, 3 are supersymmetric with the cases p = 1, 3 being well-known examples already. We construct explicit (partially smeared) brane bound state solutions for all such configurations. The D2-D4 and D(−1)-D7 cases are entirely novel, but they do not have a near-horizon AdS geometry. The two novel classes of solutions feature ghost branes (negative tension branes), and we suggest they are physical for the D(−1)-D7 solutions but unphysical for the D2-D4 solutions. The bound state of a D(−1) and a D7 brane in supergravity was only hinted upon recently in [1]. We correct the solution here in order to preserve supersymmetry, and find that the dilaton can indeed be stabilized. This points to a possible dual matrix theory, generalizing the IKKT matrix model to allow for conformal invariance.