Large Dimensions and Small Curvatures from Supersymmetric Brane Back-reaction

We compute the back-reaction of pairs of codimension-two branes within an explicit flux-stabilized compactification, to trace how its properties depend on the parameters that define the brane-bulk couplings. Both brane tension and magnetic couplings to the stabilizing flux play an important role in the resulting dynamics, with the magnetic coupling allowing some of the flux to be localized on the branes (thus changing the flux-quantization conditions). We find that back-reaction lifts the classical flat directions of the bulk supergravity, and we calculate both the scalar potential and changes to the extra-dimensional and on-brane geometries that result, as functions of the assumed brane couplings. When linearized about simple rugby-ball geometries the resulting solutions allow a systematic exploration of the system's response. Several of the systems we explore have remarkable properties. Among these are a propensity for the extra dimensions to stabilize at exponentially large sizes, providing a mechanism for generating extremely large volumes. In some circumstances the brane-dilaton coupling allows the bulk dilaton to adjust to suppress the on-brane curvature parametrically below the change in brane tension, potentially providing a mechanism for reducing the vacuum energy. We explore the stability of this suppression to quantum effects in the case where their strength is controlled by the value of the field along the classical flat direction, and find it can (but need not) be stable.