Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de Sitter space

Abstract

We consider critical gravity as van Dam-Vletman-Zakharov (vDVZ) discontinuity in anti de Sitter space. For this purpose, we introduce the higher curvature gravity. This discontinuity can be confirmed by calculating the residues of relevant poles explicitly. For the non-critical gravity of $0<m_2^2<-2\Lambda/3$, the scalar residue of a massive pole is given by 2/3 when taking the $\Lambda \to 0$ limit first and then the $m^2_2 \to 0$ limit. This indicates that the vDVZ discontinuity occurs in the higher curvature theory, showing that propagating degrees of freedom is decreased from 5 to 3. However, at the critical point of $m^2_2=-2\Lambda/3$, the tensor residue of a massive pole blows up and scalar residue is -5/36, showing the unpromising feature of the critical gravity.