Modes of log gravity

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 noncritical theory. The linearized Einstein tensor of a spin-2 log mode is itself a ‘nongauge’ 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.