Perturbative Antibrane Potentials in Heterotic M Theory

We derive the perturbative four-dimensional effective theory describing heterotic M theory with branes and antibranes in the bulk space. The backreaction of both the branes and antibranes is explicitly included. To first order in the heterotic ϵS expansion, we find that the forces on branes and antibranes vanish and that the Kachru-Kallosh-Linde-Trivedi (KKLT) procedure of simply adding to the supersymmetric theory the probe approximation to the energy density of the antibrane reproduces the correct potential. However, there are additional nonsupersymmetric corrections to the gauge-kinetic functions and matter terms. The new correction to the gauge-kinetic functions is important in a discussion of moduli stabilization. At second order in the ϵS expansion, we find that the forces on the branes and antibranes become nonvanishing. These forces are not precisely in the naive form that one may have anticipated and, being second order in the small parameter ϵS, they are relatively weak. This suggests that moduli stabilization in heterotic models with antibranes is achievable.