Quasi-Topological Ricci Polynomial Gravities

TL;DR

This paper constructs and classifies quasi-topological Ricci polynomial gravities that do not affect certain solutions but influence perturbations, with implications for holography and bounds on physical quantities.

Contribution

It introduces new classes of quasi-topological Ricci polynomial gravities, including Lovelock-like theories, and analyzes their effects on holographic properties and stability.

Findings

Linearized quasi-topological gravities are ghost-free on Einstein metrics.

Quasi-topological terms can violate holographic diffusivity bounds.

Extra massive modes from these theories can lead to unbounded butterfly velocities.

Abstract

Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ans\"atze. They therefore play no r\^ole in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where $g_{tt} g_{rr}$ is constant. The third type is the linearized quasi-topological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.