Modes of Log Gravity

TL;DR

The paper investigates the linearized spectrum of a D-dimensional critical gravity around an AdS vacuum, showing that at the critical point massive spin-2 modes coalesce with massless ones and give rise to logarithmic modes. It identifies two families of log modes, spin-2 and Proca, and constructs explicit solutions in AdS4 using the SO(2,3) symmetry, with the Einstein tensors of the log modes proportional to massless helicity solutions, hinting at a holographic dual logarithmic CFT. The authors analyze boundary-condition implications and unitarity, noting that logarithmic modes may affect the bulk and dual theory's consistency, and discuss subsequent results on energy positivity and possible non-orthogonality to Einstein modes. This work clarifies the structure and classification of log modes in higher-dimensional critical gravity and motivates further exploration of logarithmic boundary conditions and CFT duals in arbitrary dimensions.

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.