The fate of Newtonʼs law in brane-world scenarios

We consider brane-world scenarios embedded into string theory. We find that the D-brane backreaction induces a large increase in the open string?s proper length. Consequently the stringy nature of elementary particles can be detected at distances much larger than the fundamental string scale. As an example, we compute the gravitational potential between two open strings ending on backreacting D3-branes in four-dimensional compactifications of type II string theory. We find that the Newtonian potential receives a correction that goes like 1/r but that is not proportional to the inertial masses of the open strings, implying a violation of the equivalence principle in the effective gravitational theory. This stringy correction is screened by thermal effects when the distance between the strings is greater than the inverse temperature. This suggests new experimental tests for many phenomenological models in type II string theory.

D-branes are non-perturbative extended objects which play a key role in many recent developments of string theory. The elementary degrees of freedom of D-branes are open strings with endpoints attached to the D-branes. String theory has been extensively studied in the probe-brane approximation, while much less is understood when the backreaction of the D-branes is taken into account. In this Letter we compute the gravitational potential energy between open strings ending on backreacting D3-branes. We find that the D-brane backreaction yields a large correction to the gravitational potential. This happens because the gravitons exchanged between the open strings are sensitive to the geometry in the neighborhood of the D-branes, which is strongly deformed by the D-brane backreaction.

Our results are relevant for a large family of phenomenological models, which are promising candidates to embed our universe into string theory. In these scenarios, the standard model is localized on D-branes arranged in a four-dimensional compactification of superstring theory. Our computations show that an observer living on such a brane-world could detect a macroscopic violation of the equivalence principle at very low temperatures.