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

TL;DR

This paper investigates conditions for stable, ghost-free Minkowski vacua in Lovelock gravity compactifications on symmetric spaces, identifying classes of spaces that allow for genuinely stable solutions.

Contribution

It demonstrates that including cubic Lovelock terms can eliminate ghosts and achieve stable Minkowski vacua in certain symmetric space compactifications.

Findings

Inclusion of cubic Lovelock terms removes ghost instabilities.

Stable Minkowski vacua are achievable on higher-rank symmetric spaces.

Universal log-convexity among Lovelock invariants supports stability analysis.

Abstract

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.