Modes of Log Gravity

TL;DR

This paper investigates the linearized modes of a D-dimensional critical gravity theory around its anti-de Sitter vacuum, revealing the nature of log modes and their potential holographic duals in logarithmic conformal field theories.

Contribution

It classifies and analyzes the physical log modes in critical gravity, showing their origin as limits of massive spin 2 modes and exploring their properties.

Findings

Log modes arise as limits of massive spin 2 modes.

Linearized Einstein tensor of log modes is a non-gauge solution.

Proca modes' Einstein tensor resembles a gauge transformation.

Abstract

The physical modes of a recently proposed D-dimensional "critical gravity", linearized about its anti-de Sitter vacuum, are investigated. All "log mode" solutions, which we categorize as `spin 2' or `Proca', arise as limits of the massive spin 2 modes of the non-critical theory. The linearized Einstein tensor of a spin 2 log mode is itself a 'non-gauge' solution of the linearized Einstein equations whereas the linearized Einstein tensor of a Proca mode takes the form of a linearized general coordinate transformation. Our results suggest the existence of a holographically dual logarithmic conformal field theory.