Non-perturbative vacua for M-theory on G2 manifolds

TL;DR

This work systematically analyzes moduli stabilization in M-theory on compact $G_2$ manifolds using a flux-induced superpotential and membrane-instanton contributions within an approximate Kähler potential. By separating moduli into bulk $T^a$ and blow-up $U^i$ sectors and studying both universal and general toy models, it demonstrates the existence of minima with negative cosmological constant that stabilize all moduli, including both supersymmetric and supersymmetry-breaking vacua, and shows that supersymmetric Minkowski vacua are obtainable through parameter tuning. Consistency requirements demand $t^a>1$, $u^i>1$ and small blow-up corrections (small $u/t$), which in turn bound the number of blow-up moduli $I$ to a modest range; achieving de Sitter or Minkowski vacua beyond SUSY cases would require additional ingredients. The results persist when extending from universal to general models, and the authors discuss extending the framework with extra branes to realize positive cosmological constant, highlighting both the methodological advances and the remaining challenges in non-perturbative moduli stabilization in $G_2$ compactifications.

Abstract

We study moduli stabilization in the context of M-theory on compact manifolds with G2 holonomy, using superpotentials from flux and membrane instantons, and recent results for the Khaeler potential of such models. The existence of minima with negative cosmological constant, stabilizing all moduli, is established. While most of these minima preserve supersymmetry, we also find examples with broken supersymmetry. Supersymmetric vacua with vanishing cosmological constant can also be obtained after a suitable tuning of parameters.

Figures (8)

• Figure 1: Contour plot of the potential, given by Eq. (\ref{['Vu']}), in the ($t$,$\tau$) plane for $m=-1$, $k=20$.
• Figure 2: Contour plot of the potential, given by Eq. (\ref{['pot7']}), as a function of $t_a$ ($a=1,2,3$) and $t_b$ ($b=4,5,6,7$) for $m_a=4$, $k_a=200$, $m_b=-3$, $k_b=-150$. The imaginary parts of all fields have been set to zero, where we have a minimum.
• Figure 3: Plot of the potential, given by Eq. (\ref{['pot7']}), as a function of $\tau_a$, $\tau_b$ for the same values of parameters as in the previous figure. The real parts of the fields have been set to their minimum values at ${\rm ln} |k_i/m_i|$, $i=a,b$.
• Figure 4: Contour plot of the potential, given by Eq. (\ref{['V0']}), in the $t$, $u$ plane, for $m=3$, $k=1200$, $\mu=-10$, $l=-30$. We have also plotted the conditions $F_T=F_U=0$ in order to show the supersymmetric character of the minimum. The imaginary parts of all fields have been set to zero.
• Figure 5: Plot of the potential, given by Eq. (\ref{['V0']}), as a function of $t$, $u$ for the same values of parameters as in the previous figure. The minimum corresponds to Eqs (\ref{['Tval']},\ref{['Uval']},\ref{['tuningTU']}) being fulfilled.