Explaining the Electroweak Scale and Stabilizing Moduli in M Theory

TL;DR

This work provides a detailed mechanism for stabilizing all moduli in fluxless M theory on G2-holonomy manifolds via nonperturbative hidden-sector dynamics, yielding a (nearly) unique metastable de Sitter vacuum with spontaneously broken SUSY. A central result is the suppression of tree-level gaugino masses relative to the gravitino mass, which, together with anomaly-mediated contributions, produces a phenomenologically viable superpartner spectrum with TeV-scale gauginos and heavier scalars. Imposing a small cosmological constant drives the gravitino mass into the 1–100 TeV range, while the LHC signatures are predicted to be gluino-rich and distinct from Type IIB scenarios. The analysis covers both AdS and dS vacua, extends to hidden-sector matter, and shows that the resulting soft terms are largely controlled by the underlying geometric data of the G2 manifold, with robust implications for collider phenomenology and dark matter.

Abstract

In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua without fluxes, all moduli are stabilized by the effective potential and a stable hierarchy is generated, consistent with standard gauge unification. This paper explains the results of \cite{Acharya:2006ia} in more detail and generalizes them, finding an essentially unique de Sitter (dS) vacuum under reasonable conditions. One of the main phenomenological consequences is a prediction which emerges from this entire class of vacua: namely gaugino masses are significantly suppressed relative to the gravitino mass. We also present evidence that, for those vacua in which the vacuum energy is small, the gravitino mass, which sets all the superpartner masses, is automatically in the TeV - 100 TeV range.

Figures (21)

• Figure 1: Positive values of $s_1$ plotted as a function of $\alpha$ for a case with two condensates and three bulk moduli for the following choice of constants $b_1=\frac{2\pi}{30},b_2=\frac{2\pi}{29},N^1_i=\{1,2,2\},N^2_i=\{2,3,5\},a_i=\{1,1/7,25/21\}$. The qualitative feature of this plot remains the same for different choices of constants as well as for different $i$. The vertical line is the locus for $\alpha=\frac{b_2N^2_i}{b_1N^1_i}$, where the denominator of (\ref{['si']}) vanishes.
• Figure 2: Left - $A_2/A_1$ plotted as a function of $\alpha$ for a case with two condensates and three bulk moduli. The function diverges as it approaches the loci of singularities of (\ref{['si']}), viz.$\alpha=\frac{b_2N^2_i}{b_1N^1_i}$. Right - Positive $s_i,\,i=1,2,3$ for the same case plotted as functions of $\alpha$. $s_1$ is represented by the solid curve, $s_2$ by the long dashed curve and $s_3$ by the short dashed curve.The vertical lines again represent the loci of singularities of (\ref{['si']}) which the respective moduli $s_i$ asymptote to. The horizontal solid (red) line shows the value unity for the moduli, below which the supergravity approximation is not valid. Both plots are for $b_1=\frac{2\pi}{30},b_2=\frac{2\pi}{29},N^1_i=\{1,2,2\},N^2_i=\{2,3,5\},a_i=\{1,1/7,25/21\}$.
• Figure 3: Plots of positive $s_i,i=1,2,3$ as functions of $A_2/A_1$. Top Left: Same choice of constants as in Figure(\ref{['Plots2-3']}), i.e. $b_1=\frac{2\pi}{30},\,b_2=\frac{2\pi}{29},\,N^1_i=\{1,2,2\},\,N^2_i=\{2,3,5\},\,a_i=\{1,1/7,25/21\}.$ Top Right: We increase the ranks of the gauge groups but keep them close (keeping everything else same) - $b_1=\frac{2\pi}{40},\,b_2=\frac{2\pi}{38}$. Bottom Left: We introduce a large difference in the ranks of the gauge groups (with everything else same) - $b_1=\frac{2\pi}{40},\,b_2=\frac{2\pi}{30}$. Bottom Right: We keep the ranks of the gauge groups as in Top Left but change the integer coefficients to $N^1_i=\{1,2,2\},\,N^1_i=\{3,3,4\}$.
• Figure 4: Plots of positive $s_i,i=1,2,3$ as functions of $A_2/A_1$. The constants are $b_1=\frac{2\pi}{30},b_2=\frac{2\pi}{29},N^1_i=\{1,0,1\},N^2_i=\{1,1,1\},a_i=\{1/10,1,37/30\}$. $s_1$ is represented by the solid curve, $s_2$ by the long dashed curve and $s_3$ by the short dashed curve. The red curve represents the volume of the internal manifold as a function of $A_2/A_1$. Right - the same plot with the vertical plot range decreased.
• Figure 5: Plot of $\nu$ as a function of $A_2/A_1$ for the choice $b_1=\frac{2\pi}{5},\,b_2=\frac{2\pi}{4}$. The solid (red) curve represents the exact numerical solution whereas the black dashed curve is the leading order approximation given by (\ref{['nu10']}).