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Ghost-Free Stable Minkowski Vacua in Lovelock Compactifications on Irreducible Symmetric Spaces

We study the compactification of higher-dimensional Lovelock gravity on compact irreducible symmetric spaces, focusing on conditions under which a physically healthy four-dimensional Minkowski vacuum exists. We show that when the internal dimension is five or less, or when the theory is restricted to the Einstein-Gauss-Bonnet sector, the four-dimensional graviton (tensor sector) is necessarily a ghost. Inclusion of the cubic Lovelock term removes this ghost instability; however, the resulting Minkowski vacuum is generically only metastable, being accompanied by energetically favored Anti-de Sitter vacua. While such metastability cannot be avoided for spherical internal spaces, we identify an infinite class of higher-rank symmetric spaces where the true vacuum can be pushed to infinity in moduli space, thereby realizing genuinely stable and ghost-free Minkowski vacua at the level of the four-dimensional effective theory. To support these conclusions, we explicitly compute Lovelock terms up to cubic order on these spaces, confirming a universal log-convexity among the linear, quadratic, and cubic invariants, which plays a central role in our analysis.