GJMS-like operators on symmetric 2-tensors and their gravitational duals

Abstract

Abstract We study a family of higher-derivative conformal operators $$ {P}_{2k}^{(2)} $$ P 2 k 2 acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars.We first provide the alternative description in terms of a bulk Poincaré-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators $$ {P}_{2k}^{(2)} $$ P 2 k 2 in terms of the functional determinant for massive gravitons with standard and alternate boundary conditions. The analogous construction for vectors $$ {P}_{2k}^{(1)} $$ P 2 k 1 is worked out as well and we also rewrite the holographic formula for unconstrained vector and traceless symmetric 2-tensor by decoupling the longitudinal part.Finally, we show that the holographic formula provides the necessary building blocks to address the massless and partially massless bulk gravitons. This is confirmed in four and six dimensions, verifying full agreement with results available in the literature.