S-Track Stabilization of Heterotic de Sitter Vacua

TL;DR

This paper presents the S-Track mechanism to stabilize the volume modulus $S$ and orbifold-size $T$ in heterotic M-theory flux compactifications by leveraging M5-instantons wrapping the Calabi–Yau, alongside $H$-flux, open M2-instantons, and hidden-sector gaugino condensation. The stabilization is encoded in a racetrack-like superpotential that couples $S$ and $T$, leading to large, trustworthy vevs and a small, positive vacuum energy with spontaneous SUSY breaking via $D_T W eq 0$. Complex structure moduli are fixed at a high scale through warping and gaugino condensation, while vector-bundle moduli are fixed by $D_{oldsymbol{3}}W=0$, enabling a complete moduli stabilization in a de Sitter vacuum. Axions are fixed by the interference of multiple nonperturbative contributions, and numerical examples demonstrate robust stabilization with positive Hessians and nonzero $D_T W$. Overall, the work provides a concrete mechanism for achieving heterotic de Sitter vacua within a controlled low-energy EFT framework.

Abstract

We present a new mechanism, the S-Track, to stabilize the volume modulus S in heterotic M-theory flux compactifications along with the orbifold-size T besides complex structure and vector bundle moduli stabilization. The key dynamical ingredient which makes the volume modulus stabilization possible, is M5-instantons arising from M5-branes wrapping the whole Calabi-Yau slice. These are natural in heterotic M-theory where the warping shrinks the Calabi-Yau volume along S^1/Z_2. Combined with H-flux, open M2-instantons and hidden sector gaugino condensation it leads to a superpotential W which stabilizes S similar like a racetrack but without the need for multi gaugino condensation. Moreover, W contains two competing non-perturbative effects which stabilize T. We analyze the potential and superpotentials to show that it leads to heterotic de Sitter vacua with broken supersymmetry through non-vanishing F-terms.

Figures (1)

• Figure 1: Plot and contour plot of the logarithm $\ln(U d/6 M_{Pl}^4)$ of the $S$-$T$rack potential. $s$ is plotted along the x-axis, $t$ is plotted along the y-axis and we have chosen the slice $\sigma_S=\sigma_T=0$. Both $t$ and $s$ get clearly stabilized at values large enough to trust the supergravity description.