Massless Minkowski Conjecture (MMC)

Ascertain whether all ten-dimensional supergravity solutions compactified to four-dimensional Minkowski space necessarily admit at least one massless four-dimensional scalar in the universal sector (ρ, τ, σ_I).

Background

MMC links Minkowski vacua to unavoidable flat directions in the universal scalar sector; the review discusses many examples consistent with this claim and its possible relation to the de Sitter tachyon conjecture.

Despite broad empirical support, MMC remains unproven in full generality.

References

"We recall from here; an \sl Massless Minkowski Conjecture (MMC) . We recall it here \begin{gather} \label{MMC} \begin{aligned} \text{MMC}:\quad & \text{\sl 10d supergravity solutions compactified to 4d Minkowski always admit} \ & \text{\sl a 4d massless scalar, among the fields $(\rho,\tau,\sigma_I)$.} \end{aligned} \end{gather}"

— Dark energy from string theory: an introductory review  (2603.25797 - Andriot, 26 Mar 2026) in Section 3.2.3, Stability