Scanning the Fluxless $G_2$ Landscape

We show that there exists an exponentially large discretuum of vacua in $G_2$-compactifications of M-theory without flux. In M-theory-inspired $G_2$-MSSM, quantities relevant for particle physics remain virtually insensitive to large variations of the vacuum energy across the landscape. The purely non-perturbative vacua form a special subset of a more general class of vacua containing fractional Chern-Simons contributions. The cosmological constant can be dynamically neutralized via a chain of transitions interpolated by fractional gauge instantons describing spontaneous nucleation of M2-brane domain walls. Each transition is generically accompanied by a gauge symmetry breaking in some sector of the theory. In particular, the visible sector GUT symmetry breaking can likewise be triggered by a spontaneous nucleation of an M2-brane.