Nonlinear Dynamics of Parity-Even Tricritical Gravity in Three and Four Dimensions

TL;DR

This paper investigates the nonlinear behavior of parity-even tricritical gravity in three and four dimensions, revealing that the classically expected unitary subspace is unstable when nonlinear effects are considered.

Contribution

It extends the analysis of tricritical gravity to the nonlinear regime, demonstrating the absence of the unitary subspace due to linearization instability.

Findings

Unitary subspace is absent in the full nonlinear theory.

Linearization instability affects the would-be unitary sector.

Nonlinear effects destabilize the tricritical gravity solutions.

Abstract

Recently proposed "multicritical" higher-derivative gravities in Anti de Sitter space carry logarithmic representations of the Anti de Sitter isometry group. While generically non-unitary already at the quadratic, free-theory level, in special cases these theories admit a unitary subspace. The simplest example of such behavior is "tricritical" gravity. In this paper, we extend the study of parity-even tricritical gravity in d = 3, 4 to the first nonlinear order. We show that the would-be unitary subspace suffers from a linearization instability and is absent in the full non-linear theory.