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

TL;DR

This work investigates the healthiness of four-dimensional Minkowski vacua arising from Lovelock gravity compactified on compact irreducible symmetric spaces (CIRS). It shows that no-go results plague only the Einstein–Gauss–Bonnet sector, while including a cubic Lovelock term can yield locally ghost-free Minkowski vacua, which are typically metastable due to an energetically favored AdS vacuum. A universal log-convexity among Lovelock invariants drives these stability structures, and a kinetic-barrier mechanism, available only for higher-rank CIRS spaces, can push AdS vacua to infinite moduli distance, yielding genuinely stable, ghost-free Minkowski vacua in an infinite class of spaces. The results illuminate a structural AdS-prone landscape in Lovelock compactifications and identify precise geometric conditions under which viable vacua may exist, with implications for cosmology and phenomenology. They also reveal deep mathematical properties of Lovelock densities on CIRS spaces and motivate further exploration of higher-order terms and quantum effects on vacuum stability.

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.

Figures (7)

• Figure 1: $\hat{d}$-dependence of the Gauss-Bonnet term (left) and the cubic Lovelock term (right).
• Figure 2: $\hat{d}$ dependence of the log-convexity strength $\mu$. Data for $S^n$ and $\mathbb CP^m$ are located on the bottom layer of this figure.
• Figure 3: Schematic illustration of the kinetic barrier mechanism. The moduli space is divided into three regions: the Minkowski region(green), the ghost region(red), and the AdS region(orange). The wavy lines indicate the physically accessible domains. The divergence of the kinetic term at the boundaries of the ghost region creates a barrier that geodetically isolates the Minkowski vacuum from the AdS region.
• Figure 4: Stabilizable spaces in the allowed region (light green) are shown in the left panel, and the width of the stable window for each case is displayed in the right panel.
• Figure 5: Coefficients $A_0({\cal \hat{M}})e^{\beta \hat{d}/2}$ (left) and $B_0({\cal \hat{M}})$ (right) for stabilizable CIRS spaces, plotted as functions of the internal dimension $\hat{d}$ for various classical series.