On the Effective Potential of the Dp- anti Dp system in type II theories

TL;DR

This work provides a concrete tree-level computation of the effective potential for a parallel $Dp-\overline{Dp}$ system in type II theories, demonstrating tachyon condensation and a vacuum structure where transverse scalars obtain VEVs proportional to the brane separation. By embedding the system in a toroidal background with constant Wilson lines and carefully matching open-string amplitudes to a low-energy field theory, the authors derive the quartic tachyon coupling $\lambda=\frac{e^2}{2}$ and the couplings $\nu_{ab}=\overline{\nu}_{ab}=\widetilde{\nu}_{ab}=e^2\delta_{ab}$, all as functions of the separation and the gauge coupling. The analysis reveals that tachyon condensation occurs across distances, breaking the $U(1)$ sectors and giving mass to certain gauge and scalar modes, with the relative transverse fluctuation $\phi-\overline{\phi}$ acquiring a distance-proportional VEV. This supports the interpretation of brane–antibrane binding via tachyon dynamics and clarifies the fate of gauge degrees of freedom after condensation in both distinguishable and indistinguishable brane scenarios. The results have implications for understanding non-BPS configurations and the microscopic realization of Sen's tachyon condensation picture in a controlled CFT framework.

Abstract

We compute the effective potential of a system composed by a Dp brane and a separated anti-Dp brane at tree level in string theory. We show explicitly that the tachyon condenses and that the scalars which describe transverse fluctuations acquire a VEV proportional to the distance.