On unitary subsectors of polycritical gravities

TL;DR

This paper investigates higher-derivative gravity theories at critical points, analyzing their linearized perturbations, boundary behaviors, and the potential for unitary truncations, with implications for dual logarithmic conformal field theories.

Contribution

It characterizes the linearized modes and boundary behavior of polycritical gravities and demonstrates possible unitary truncations at the linearized level for odd rank.

Findings

Linearized modes exhibit Jordan block structure.

Inner products are non-unitary.

Existence of unitary truncations for odd rank.

Abstract

We study higher-derivative gravity theories in arbitrary space-time dimension d with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to be dual to logarithmic conformal field theories in the (d-1)-dimensional boundary of an AdS solution. We determine the structure of the linearized perturbations and their boundary fall-off behaviour. The linearized modes exhibit the expected Jordan block structure and their inner products are shown to be those of a non-unitary theory. We demonstrate the existence of consistent unitary truncations of the polycritical gravity theory at the linearized level for odd rank.