Perturbative Anti-Brane Potentials in Heterotic M-theory

TL;DR

This work derives a perturbative four-dimensional effective theory for heterotic M-theory with branes and a bulk anti-brane by reducing on a non-supersymmetric five-dimensional domain wall. At leading order in the strong-coupling expansion, the SUSY-like 4D action is completed by an uplifting potential ${ m V}_1$ that depends on the dilaton and Kahler moduli and is independent of brane positions, consistent with probe-brane expectations. At next order ${f O}( vert oldsymbol{ extepsilon} vert^2)$, nontrivial inter-brane forces emerge, including a novel back-reaction term, and there are threshold corrections to gauge kinetic functions that break holomorphy due to SUSY breaking; all such effects are suppressed and open the possibility for moduli stabilization via a balance with non-perturbative effects. The results are cross-checked through dual descriptions and a simple example, and they have important implications for SUSY breaking, cosmology, and gaugino condensation in heterotic setups with anti-branes.

Abstract

We derive the perturbative four-dimensional effective theory describing heterotic M-theory with branes and anti-branes in the bulk space. The back-reaction of both the branes and anti-branes is explicitly included. To first order in the heterotic strong-coupling expansion, we find that the forces on branes and anti-branes vanish and that the KKLT procedure of simply adding to the supersymmetric theory the probe approximation to the energy density of the anti-brane reproduces the correct potential. However, there are additional non-supersymmetric 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 strong-coupling expansion, we find that the forces on the branes and anti-branes become non-vanishing. These forces are not precisely in the naive form that one may have anticipated and, being second order in the small parameter of the strong-coupling expansion, they are relatively weak. This suggests that moduli stabilization in heterotic models with anti-branes is achievable.

Figures (3)

• Figure 1: The brane configuration in five-dimensional heterotic M-theory
• Figure 2: Warping of the Calabi-Yau volume modulus V (bracket on the RHS of \ref{['V']}), assuming $h^{1,1}(X)=1$. The dashed, red curve corresponds to a BPS configuration with one brane at $z=1/4$ and charge vector $(\beta^{(p)})=(1,2,-3)$. The solid, green curve describes a situation with one brane at $z=1/4$, one anti-brane at $z=3/4$ and charge vector $(\beta^{(p)})=(1,2,-5,2)$. It can be obtained from the previous BPS configuration by "pulling" an anti-brane with charge $-5$ off the boundary at $z=1$.
• Figure 3: Anti-brane potential in the absence of other branes (from the bracket on the RHS of \ref{['VY']}), assuming $h^{1,1}(X)=1$. The solid, green curve corresponds to charges $(\beta^{(p)})=(3,-2,-1)$. In this case the anti-brane is attracted to the positively charged boundary at $z=0$. The red, dashed curve corresponds to charges $(\beta^{(p)})=(2,-3,1)$. The anti-brane is attracted to either one of the boundaries, depending on its position $z$.